Meep, I used to be good at this stuff but coming up with anything original while still trying to make sense is really difficult.
Have you considered using different languages though? A couple of the species in my fantasy are loosely based on ancient cultures, particularly the Greeks, so I looked up words in a translator and edited the results slightly.
For example, here's how I operate when trying to come up with alternatives:
I stopped by
Behind the Name to search names with the meaning "secret". Of the list that came back, my favourite was the Norwegian
Dagrun, so then I went to
iTools look up "clan" in Norwegian. I got
klan back and quite like the idea of the
Dagrun Klan.
It seems out of context for your Magi society, though, and I'd probably go with something Latin or Classic because they seem more arcane to me. But that's just me, so... Maybe try searching Behind the Name like I did, or iTools translations, and see what you get? It can be fun just seeing the combinations you can come up with. >D
You can also search the meaning on BtN, which could be handy? I searched for "dragon" and came up with
Tiamat. I'd be tempted to combine it with Marduk, a god who killed Tiamat, to make the Tiamat Marduk society. XD Depending on the context, it could make a cool name. Or I could just be weird, I dunno. ¬_¬
Oh and did I mention changing the spelling, or editing slightly? You could have Dragūn Klan (that's a poor example ¬_¬) or Tiamarduk or whatever makes sense to you.
Ooh, another alternative.
Seventh Sanctum has a lot of generators. Some of them are a bit on the silly side (Ancient Kingdom of Counties, wah? lol) but you can get some good ideas from the generated lists, or mix and match. :)