There are preset traits, but there is a subtle variance to them of one or two that change on most if not all npcs. Not all I think some are absolutely locked. Felix isn't completely locked but I might be wrong, but like Bud, not sure if he changes bratty, Felix will always have bratty? I think you can roll a few others different in the mix. Ansel and Evelyn, had the same ones.
They've made it easier now to roll different traits, that variance. Just save your game, buy, and teleport back to house, repeat. Others like Michelle, buy her flat out first. Add her later. Int girl, on the ring quest from Raikan, kill the punks capture cybergirl. Leave her there. Save, and above. The same as Astrid, in the tower. Nicole it took a few rolls is a brawler/warrior. Never used her for arena before but she has an animation, get in there.
Always save before you buy.