Was Arwen called Evenstar at birth?

Question

After seeing the the question about Arwen's association with the night I thought about Arwen's nickname, Evenstar (Undómiel) - it being a reference to the last rebirth of the beauty of the Elves (i.e. Luthien) before their final departure. Giving her that nickname must mean that the Elves understood and accepted the approaching end.

I am not sure whether this nickname was given to Arwen at birth. If it was - although that's somewhat presumptive for a baby - then the Elves must have by then come around to fully accepting their end, and that's nearly three millennia before the LotR takes place. Which seems rather early for having thrown in the towel, especially since the development of Men, even during the LotR, gives little hint of a coming Renaissance. Not to mention that six or so thousand years ago was still the First Age.

It might be more reasonable to assume the nickname was given to Arwen later in life, but I can't seem to find solid information on that. I'd like to find out if that's something we know.

Answer 1

No she was not given it at birth.¹

Taking a quick look at every instance of the name "Evenstar" or "Undómiel", it appears she was always named it, as far as the timeline of The Lord of the Rings is considered, but considering she's over 2000 years old at the time she could've been given the name at any point over those years.

¹ If we are willing to trust TolkienGateway, Undómiel was an epessë, which according to the Unfinished Tales is:

epessë   An ‘after-name’ received by one of the Eldar in addition to the given names (essi).
_{Unfinished Tales: Index}

The description of an epessë is given earlier in the text, in which the naming conventions of the Eldar of Valinor are given. While Arwen is not of the Eldar of Valinor, and neither of her parents were born in Valinor, her mother was of the people of the Noldor.

It is said in an essay concerning the customs of name-giving among the Eldar in Valinor that they had two ‘given names’ (essi), of which the first was given at birth by the father; and this one usually recalled the father’s own name, resembling it in sense or form, or might even be actually the same as the father’s, to which some distinguishing prefix might be added later, when the child was full-grown. The second name was given later, sometimes much later but sometimes soon after the birth, by the mother; and these mother-names had great significance, for the mothers of the Eldar had insight into the characters and abilities of their children, and many also had the gift of prophetic foresight. In addition, any of the Eldar might acquire an epessë (‘after-name’), not necessarily given by their own kin, a nickname – mostly given as a title of admiration or honour; and an epessë might become the name generally used and recognised in later song and history.
_{Unfinished Tales - Part Two: The Second Age, IV: The History of Galadriel and Celebron}

From the above it is clear that she was certainly given the name after birth, however, how long after birth is unclear. We know she has the name when Aragorn meets her when he's in his 20s. So she could've received the name at any point between TA 241 to TA 2951. So anytime up to her 2710th year.

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“Estel I was called,” he said; “but I am Aragorn, Arathorn’s son, Isildur’s Heir, Lord of the Dúnedain”; yet even in the saying he felt that this high lineage, in which his heart had rejoiced, was now of little worth, and as nothing compared to her dignity and loveliness. ‘But she laughed merrily and said: “Then we are akin from afar. For I am Arwen Elrond’s daughter, and am named also Undómiel.
_{The Return of the King - Book VII, Appendix A: V, Here follows a part of the tale of Aragorn and Arwen}