'He called her by her Elvish name'

[Elmo]

In the part of the Lay of Leithien that Aragorn sings to the Hobbit, after Beren cried 'Tinuviel, Tinuviel' The next line in the song is 'He called her by her Elvish name'. This is strange as it is if Beren is calling her by a name that she already has when I'm sure it was Beren that first called her 'nightinggale'. If it was Beren who first called her this, does this mean that 'Luthien' is not an Elvish name. Then is it Valarien?

[Aiwendil]

I'm fairly sure that: 1. Beren was indeed the one who first named her "Tinuviel" and 2. "Luthien" is a Sindarin name.

I can't recall sources for either of those two assertions at the moment, but I'm fairly sure that they exist. I'll check HoMe for them later.

I'd say that "he called her by her Elvish name" is just a bit of misleading poetic license. It's a true statement, as far as it goes; it just omits to mention that, in fact, both of her names are Elvish and that the name he called her was his own invention.