Their class names are mostly bird related; hawks, eagles, and the like everywhere.
I've only actually used the Drazi about half a dozen times, but if I was going to, I'd probably run with that as a theme.
The obvious for the capital- Hawk, Condor, Kestrel should be nothing less than Stormfalcon- class. You can get ever more obscure bird names as you go down the scale. Thousands to choose from.
(none of them with a decent F arc, but hey, upside, downside...)