There's no rules against having duplicate names. To be Generic Player it is usually offensive, Chris, or has other server name in it.
Was trying to make two characters. One called "Red Mage" another called "Green Mage" both ended up as generic player. I have never and would never make a silly offensive name.
That's an odd one. I could only suggest UO maybe thinks they're NPC shopkeeper impersonation attempts with the 'Mage' part of the name?
I may be wrong, but i do believe that if your toons get called Generic Player you can page a GM and get the name changed for free as long as the new name is acceptable, saves you waiting 7 days to play that toon