Hi! If you refer to the following chart you can write
Arwen with...
Tengwar CharactersVowel A -- not numbered in the chart but looks like a Roman C. See 'Additional letters' in the link.
number 25
number 24
number 35
number 21
The name will look a little bit like (using mostly Roman characters): cyu^n... well not exactly of course! as 24 has a line closing the top of the u shape for example.
This is the Mode of Beleriand. Incidentally this is the way it's written in the films (inscription for Arwen's sword).
And yes Arwen would speak Sindarin as a birth tongue (the type spoken in Rivendell). I would say she probably knew Quenya as a 'book language', as Quenya '
... had become, as it were, an 'Elven-latin', still used for ceremony, and for high matters of lore and song.'Glad to help Wisprilla!
And obviously you can make the writing fancier than what appears in the chart (the basic shapes of the Elvish characters), depending upon the style of lettering you choose.
Check out some examples at
Amanye Tenceli on the web (if you like).