There are many ways that you could come up with a name, depending on what suits your style.You can find words that have meaning to your character and maybe even translate it into Elven. Such is how I have "Celemegil", from "celeb" and "megil".
If you don't care so much for a "real" Elven name, and instead just want something that sounds Elven, you can try downloading the Everchanging Book of Names--a program that randomly puts syllables together to come up with names that sound like they came from the language, but are actually just gibberish.
You can do a combination of these, or different methods, which I'm sure others wouldn't mind mentioning.
--Brisid
> How do I come up with a name for my elf? Is the name Arwen taken?