In the Greek New Testament, Hell is referred to by three names, two Greek (Hades, Tartarus) and one Hebrew (Gehenna). But in English, it becomes Hell.
This is related to the Old Norse hellir, and proto-Germanic hallo, meaning cavern or enclosed space, but why is this term adopted instead of using the Greek or Hebrew terms?
How do Norse ideas of Hel as a place relate to Christian ideas of Hell?
Discourse to the Greeks Concerning Hades
As you have observed, three different New Testament terms have been popularly flattened into a singular English "Hell." Part of this mixup goes back at least to the 200s AD, when certain writers began to generalise and then systematise these different notions into the concept of a singular location in which human beings exist after their death.
From around the 800s AD, the Discourse to the Greeks Concerning Hades was misattributed to the 1st-century AD Roman Jewish author Flavius Josephus. However, it is now believed to have been written by a Christian clergyman called Hippolytus of Rome (170-235 AD, best known for his Refutation of All Heresies). This Discourse refers to Hades as the subterraneous abode of all the dead, the same function served by Hades in Greek mythology, but the text distinguishes different compartments of the netherworld, the main focus being on segregating the "just/ righteous" and the "unjust/ unrighteous," which, again, is, to an extent, a feature of the original Greek Hades.
The Discourse's description of Hades is clearly an elaboration of the rather cursory reference to it that Jesus makes in the story he tells about two men, one rich and the other poor, who die, in Ch. 16 of the Gospel of Luke (popularly known as the Parable of the Rich Man and Lazarus). Elements from other portions of the New Testament have been thrown into the Discourse's mix, fiery allusions being a favourite, most especially the Lake of Fire from the Book of Revelation a.k.a. the Apocalypse of John. In Revelation 20, Hades is cast into the Lake of Fire (and presumably consumed and destroyed therein) but in Hippolytus's Discourse the Lake of Fire is merely a section of Hades.
The Fusion of Hades and Gehenna
From hence forward in time it seems that any New Testament reference to fire connected with pain, shame or censure was early on associated with the realm of the dead in the most negative senses possible. Three of the twelve New Testament references to Gehenna link it with fire. Gehenna is actually a geographical spot very much in this world. As admitted in the ChristianCourier.com article which your Question is linked, Gehenna is "a ravine on the southern side of Jerusalem", which Michael R. Burch reports, on TheHyperTexts.com, as being, at present day,
a lovely park and tourist attraction. Wonderful archeological discoveries have been made there, such as the healing pool of Siloam and the oldest Bible verses ever discovered, inscribed on small silver amulets. Those verses are the benediction "The LORD bless thee and keep thee; the LORD make his countenance to shine upon thee and be gracious unto thee."
In spite of the fact that Gehenna is a literal valley in the world of the living, the concept of a fiery Gehenna in some otherworldly location, whose purpose is the post-mortem punishment of humans, seems to have become quite deeply ingrained in Christian cultures, especially in the Middle East, at least by the 7th century AD. This appears to be evidenced by the fact that during that era, right from the advent of Islam, Jahannam, the Arabic form of the word Gehenna, became the basic name for the Islamic version of "the bad place," deriving much of its influence from Arabian Christianity.
Even Isaac of Nineveh (a.k.a. Isaac of Syria), a Christian bishop of Arabia who lived at that time, and who himself believed that eventually all creation (even people in "the bad place") would be fully reconciled to God, referred to the bad place simply as Gehenna (or rather a close Syriac Aramaic equivalent, like Gīhannā) or Jahannam. A few centuries later, the four canonical Gospels were translated into a few different dialects of Anglo-Saxon, wherein Hades and Gehenna, apparently thought of as part of the same continuum at this point, are almost always translated uniformly as helle. Later on, as the offspring of Anglo-Saxon, the English language naturally then turned up "Hell" for its own renditions of both Hades and Gehenna.
The Abyss
Strictly speaking, the word Tartaros [Tartarus] does not appear in the New Testament. The word which does appear, ταρταρώσας (tartarōsas), occurs only once in this part of the Biblical canon, and is, according to Wikipedia, "a shortened form of the classical Greek verb kata-tartaroo", which means to "cast down [in]to Tartaros." John Wycliffe's 1385 English New Testament translates the expression as "to be drawun doun... in to helle". Subsequent English versions have generally followed suit with something along the lines of the 17th-century King James Version's "cast... downe to hell". The Rheims Bible, also produced during the reign of King James, renders this as "drawn down... to the lower hell".
Hidden Beneath
It seems to me that indeed "Hell" is the neatest, most concise English idiom for Hades. As your noted etymology indicates, the word "Hell" originally has something to do with hiding something by covering it up. This incidentally is exactly the same notion behind the Greek Hades. Consider how in Greek mythology a major attribute of the god Hades is a cap which makes him invisible, thus hiding him.
It makes perfect sense, then, that in the Ancient Greek translation of the Tanakh (commonly called the Old Testament), the word Sheol is almost always rendered as Hades, as it has the exact same connotations. They are each understood as the place where everyone goes after death, and each of them exists in a vertically layered universe in which this realm is contained—concealed—within the earth, beneath the lands of the living. And this is what Anglo-Saxon and Old English helle simply meant originally.
Things get hairy, however, with the mashing together of Gehenna and "Tartaros" with "Hell." In the case of the Tartaros-related reference, the logical step to it becoming simply "hell[e]" is traceable to the fact that, in the mythology from which the Greek term derives, Tartaros is a part of Hades, the deepest portion thereof. So if Hades = Hell, then Tartaros is the bottom of Hell. And already by the time the New Testament was being composed, in Latin literature (e.g. in the writings of Hyginus) Tartarus had simply become a common name for the abode of the dead in general and not just the lowest region of the Underworld.
Fire and Ice
There is barely any correlation to be found between the fiery notions of this "Hell" and the Hel which appears in Norse primary sources. The Norse Hel is perpetually an icily frigid world. Hell, as understood by most Christians throughout the centuries, is constantly ablaze. (The sole exception that comes to mind is the last of the nine circles of Dante Alighieri's "Inferno," which circle is a frozen lake.) While Hel is unpleasant, unlike Hell, it is not a place of punishment (i.e. when Hell is = Gehenna or Tartaros), and is simply the consequence of dying by a means other than being cut down in battle.
A slight similarity might exist between the final states of Hell and Hel. As mentioned above, in Revelation 20, which seems to envision something occurring at the climax of human history as we presently know it, Hell (together with Death) will be destroyed in a cosmic fire, from which the entire universe will be reborn or resurrected, "new heavens and a earth" in the next chapter. Before Death and Hell are cast into the Lake of Fire, however, they are emptied of the dead which are in them. In the Gylfaginning, a great fire will "burn the whole world" (just the Earth, or including Hel?), and afterwards a new world will emerge from the destruction. At this point two dead gods resurrect out of Hel to rule the new world.
Sheol in St Ephrem's Song
The most striking parallel between Hell and Hel that I can think of comes, not from the Bible, but from the hymns of another Middle Eastern Christian clergyman, namely Ephrem the Syrian (300s AD). There are a few different interpretations among Christians of what Jesus did between the time that he died and the time he resurrected. An event called the Harrowing of Hell is often named as at least one activity in which he engaged, either emptying Hell of the dead who were trapped within or at least transforming into paradise the portion of it inhabited by those considered to be saints.
The 37th of the Nisibene Hymns of St Ephrem the Syrian dramatises this by having Death weep for Sheol upon the loss of all her inhabitants. As mentioned above, Sheol is the original Hebrew term for Hell, and is the same in Ephrem's language: Syriac Aramaic. In Greek, Hades is a masculine term, and, unsurprisingly, personified as a male deity. Especially in Eastern Orthodox Christianity, which is heavily influenced by the Hellenisation of the Eastern Roman Empire, Hades is sometimes personified as a cosmic entity who gulps down all the dead, and hence did so to Jesus upon his death. But since Jesus could not be contained by the Underworld, Hades was forced to disgorge him. Hades could thus easily be interpreted as vomiting forth the dead in Revelation 20.
In Hebrew and Syriac, however, Sheol is a feminine term, and so, while St Ephrem personifies Sheol in much the same way as the Eastern Roman Christians conceptualised Hades, his hymn's cosmic Underworld personage is female. Rather than regurgitating the dead who resurrect, Nisibene Hymn 37 has Sheol giving birth to Jesus.
But lo! The Virgin has brought Him forth, and Sheol the barren has brought Him forth; two wombs that contrary to nature, have been changed by Him; the Virgin and Sheol both of them. The Virgin in her bringing forth He made glad; but Sheol He grieved and made sad in His Resurrection.
Ephrem's Sheol is female while the Norse realm of Hel is ruled by a female deity, after whom it is named. Sheol mourns the "birth" of her "reverse children," the resurrecting and escaping dead. Hel is most reluctant to let her own dead go, and in the one story in which an attempt is made to resurrect Balder, the recently deceased god of light, Hel stipulates that this will happen only if the entire cosmos mourns his demise. This plan fails and Balder is only released after the universal conflagration at the end of time. He is one of the two dead gods who returns from Hel's realm after the entire world perishes.
The word "hell" came into existence sometime before 900 AD/CE. It is from the "Middle [and] Old English hel(l); cognate with Old High German hell(i)a (German Hölle), Old Norse hel, [and] Gothic halja". 1
Being that the first English translation of the Bible was written (by John Wycliffe) in 1380's,2 the word hell was already in use by then. Just as the apostles didn't create a new word to describe hell but instead used common words like Hades and Tartarus, early translators may have decided to use the already common word hell to help the people understand the Scriptures and not be as confused.
