Maybe the medieval culture actually has a fanatical devotion to magic, and shuns technology on principle. That would explain why there's a massive technology gap. 

As for steampunk: Probably exactly as you said: cultural preference more than anything. Probably steampunk tech can do most of the same things as cyberpyunk, just in a much different way. 

Empire names:

Steampunk:
Mistvale(an allusion to the ever present steam clouds in the air)
Avolire

Magical:
Avalon
Aurelia

Cyberpunk:
Ecrion
Zoze

Just some random possibilities. 

What does Mercenary Inc do, and why are they allowed to do it?