I like the idea of mothership-type-number: Raven-S-1 for Raven’s Shuttle 1 (and we could squawk that as Raven Sierra 1 on TeamSpeak), for example, on the “official name” so it makes it obvious on the Science screen what the contact is and who it belongs to.
If we want to do “themed” ship names, I suggest that it be internal to the ship’s crew and limited to their communications – Viper-F-1 or maybe its pilot may be colloquially known as Cobra on their bridge. (“I said, ‘As_P_!'” made me giggle a little when I thought about different fighter names for Viper.)
I do like the idea of squad names and pilot callsigns (I get a little nostalgic for Space: Above and Beyond when serving on a carrier and think that we need to “deal out the Wildcards” when the fighters launch), but we won’t have to deal with things like that unless we see an uptick in membership to actually crew a squadron (and officers who don’t object to the mere thought of incorporating fighters into the canon game).