Well, I just finished writing a Shadow Chasers adventure featuring Githyanki and Githezari.
I made both of the Gith leaders multi-class characters. This gave them a cool title for thier name, straight from Manual of the Planes. The Githyanki is Gish Zazoz and the Githezari is Zerth Ra'Honic. When making up the names, I tried to use a lot of the letters found in the names of both races (z, h, a, etc...).
As far as alignment goes, Githezari tend to be monks most of the time, so this usually nescessitates a lawful alignment, at least at some point in thier career.
Also, if you're going to send your PCs to the Astral Plane to find these Gith, check out the most current free map over at the WotC site. It is the floating head of a dead god in the Astral Plane.
Good luck, and have fun!