Besides the suggestions hS has already made, I suppose she could potentially be vas [number on her RC]. It's a bit awkward, but it would make sense, if we choose to interpret Headquarters as her new fleet and all the RCs as individual ships.
As for whether or not she has to change her name, I'm afraid I have no suggestions. I can't remember anything about Quarians who have chosen to leave the Fleet permanently, so I don't know what they would be called. I guess that makes it a personal decision for you/her, which could reflect how she feels about her old home and her new life.
Also, I don't know if you already know what her old ship was, but if not, have you considered having her come from the ship Qwib Qwib? It would make for a wonderful injoke.

The best guide for the 'vas [What]' question would seem to be Tali'Zorah. The Mass Effect wiki suggests that her name changes from vas Neema to vas Normandy, which suggests that there are circumstances in which she'd change her 'surname'. I don't know the canon, but I'd suspect that a permanent change would induce a name change. Whether it would be to vas PPC, vas Protectors, vas Headquarters (possibly my favourite), or vas [Department name], would probably be up to her - since I doubt she'd be telling the, uh, Flotilla(?) about her new job.

As for given and clan names... I don't see any clear distinction between how the two are formed (for instance, 'Feda' is a given name, 'Nara' a clan, and similarly 'Zaal' is a given, 'Raan' a clan). Based on the names in 'Notable Quarians', we can deduce the following:

-Names start with a consonant, not a vowel - though this doesn't extend to ships.
-As you say, they don't go beyond a couple of syllables, and tend towards a CVCV(C) format - though the Consonants may be clusters, the Vowels may be doubled, or clustered, and there are a scattering of CVC - and even one CV - names.
-'Ys' is a consonantal sound (since it's used at the start of a name).
-'-ah' is a distinct terminal sound to '-a'.
-The letter C is not used, and I don't see W either. The most common consonant seems to be K.
-U is not used, and O and I are fairly uncommon.
-A and E are common, and can both appear as double letters, and as the cluster AE.
-Known consonant clusters are YS, SH, ZH, BR, and KH. MM, NN, RR, and DD also appear.
-At least one character (Keenah'Breizh) has a very... well, lazy name. The first half is one letter away from the invocation 'keelah', while the second half is the Breton name for Brittany. Actually, I take back 'lazy' - given the existence of a ship named Normandy, I think there's a Northern France theme here. (Which immediately suggests the clan name 'Kernow' - Cornwall - to me)

I dunno. Anything useful there?

hS