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?
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.