Did the Valar refer to themselves as Valar or was that just a name given to them?

Question

Did the Valar refer to themselves as Valar, or was "Valar" just a name given to them by the Elves because they needed a way to refer to them? Or did Eru name them before they entered into Arda?

Answer 1

The name was given by the Elves:

The Great among these spirits the Elves name the Valar, the Powers of Arda, and Men have often called them gods.

^{The Silmarillion II Valaquenta}

A list of words Quenya borrowed from Valarin is given in The War of the Jewels; "vala" is noted thus:

Vala 'has power' (sc. over the matter of Ea), 'a Power'; pl. Valar, 'they have power, the Powers'. Since these words are from the point of Q[uenyan] structure verbal in origin, they were probably versions of V[alarin] words of verbal meaning.

^{History of Middle-earth XI The War of the Jewels Part 4: "Quendi and Eldar" Appendix D: "* Kwen, Quenya, and the Elvish (Especially Ñoldorin) words for 'Language'" Note on the Language of the Valar.}

Whatever word the Valar and Eru use to describe themselves collectively (and they must have such a word) is translated to "Valar" by the Elves, and then by the translator of The Silmarillion. Consider, for example:

Then Manwë awoke, and he went down to Yavanna upon Ezellohar, and he sat beside her beneath the Two Trees. And Manwë said: 'O Kementári, Eru hath spoken, saying: "Do then any of the Valar suppose that I did not hear all the Song, even the least sound of the least voice?

^{The Silmarillion III Quenta Silmarillion Chapter 2: "Of Aulë and Yavanna"}

What relation the Quenya "Valar" has to the Valarin origin is unknown.