Can I restore a backup and then begin backing up to a new name? I'm getting an ipad mini and I already have an ipad. I'd like to restore from icloud onto the mini so I can get my apps and savegames, but after that I'd like to diverge the backups so I can configure them both differently.

I know I can restore from backup onto the new device - after I do that, will it keep the backups separate? Or will the two devices be fighting over the same icloud backup name?
They are still two separate devices. Restoring from a backup does not change that. So the next time each one runs a backup, it will be done separately, even if the devices have the same name. (That said, I would suggest for ease of identification, you change the name on one.)