Yes you can get it in an Inn room. Inn is unlocked at level 10 and if you 'retire' to a room you'll see the summoning bell for retainers and beside another summoning bell for the (hairdresser) Aesthetician I think it's called? At a cost of 2000 gil you can change hairstyle, hair color, tattoos, lip color, a few other things I forget. It's one of the styles available there.