Arwen Undómiel , also known as "Evenstar" (or Evening Star), became mortal by choice and her "fate became tied to the outcome of the ring" (words of Elrond in the movie, don't remember how that was conveyed in the book).
Once the ring is destroyed and the Fellowship is back at Minas Tirith, she is referred to as the Morningstar. How come?
Gimli is only saying poetically that he prefers Galadriel to Arwen. Arwen is never referred to as "the Morningstar". You may be confused by the dialogue between Gimli and Éomer:
‘But first I will plead this excuse,’ said Éomer. ‘Had I seen [Galadriel] in other company, I would have said all that you could wish. But now I will put Queen Arwen Evenstar first, and I am ready to do battle on my own part with any who deny me. Shall I call for my sword?’
Then Gimli bowed low. ‘Nay, you are excused for my part, lord,’ he said. ‘You have chosen the Evening; but my love is given to the Morning. And my heart forebodes that soon it will pass away for ever.’
The Lord of the Rings: The Return of the King, Many Partings, p. 305
Arwen's epessë ("after-name") is Undómiel, meaning "twilight star". It was translated into English as "Even[ing]star". There is no real explanation as to why Arwen was named "Evenstar", but my understanding (which may be wrong) is that it has two purposes:
As for Gimli's answer above, it is a play on Arwen's epessë and the relative age between Arwen and Galadriel. At the time of the War of the Ring, Arwen is roughly 2,700 years old, but Galadriel is much older. Her age is not clear because she was born in Valinor before the Years of the Sun, but she could very well be over 10,000 years old.
Being born at the beginning of the Third Age, Arwen would represent the Elves' "evening", at the end of a long and tiresome day, while Galadriel would represent the Elves' "morning", when "the light of Aman was not yet dimmed in their eyes, and they were strong and swift, and deadly in anger, and their swords were long and terrible." Galadriel's golden hair also invokes images of a golden sun in the morning, compared to Arwen's dark hair.
Arwen’s sobriquet does not change from Evenstar to Morning-star
Arwen Undómiel, known as the Evenstar (or Evening-Star), being half-elven, is given the choice between becoming Mortal (like her uncle, Elros) or remaining an Elf and passing into the west (like her father, Elrond). She eventually chooses that “Doom of Men” and becomes mortal to marry Aragorn.
Gimli, when speaking to Éomer, has a disagreement regarding the Lady of Lórien, which refers to Galadriel who is the grandmother of Arwen Undómiel. Éomer believes tales that Gimli finds disrespectful to one whom Gimli regards as the greatest beauty in Middle-earth: Galadriel, the Lady of Lorien. The dispute is eventually resolved in The Return of the King when Éomer and Gimli have this interaction when Arwen and Galadriel are both in Minas Tirith following the destruction of the One Ring:
But first I will plead this excuse,’ said Éomer. ‘Had I seen her in other company, I would have said all that you could wish. But now I will put Queen Arwen Evenstar first, and I am ready to do battle on my own part with any who deny me. Shall I call for my sword?’ Then Gimli bowed low. ‘Nay, you are excused for my part, lord,’ he said. ‘You have chosen the Evening; but my love is given to the Morning. And my heart forebodes that soon it will pass away for ever.’
Basically what’s going on is that Éomer agrees that Galadriel is of great beauty, but Arwen is “first” to him. I believe the “morning” portion is a play on words by Gimli (who is quite loquacious, especially around and regarding things of great beauty) due to Arwen being the Evening-Star and Galadriel having flowing blonde hair — not to mention the silver dawn-like descriptions of Lothlórien in winter.
I have searched the texts and appendices and have not found the word Morningstar, although I could have missed it. This brings up an interesting question: since Morningstar is a euphemism for Lucifer (at least it is now), would the devout Catholic Tolkien have used such a description?
