I voted for For the Love of Dog. Mostly because there's a grooming shop here in Calgary called Oh My dog and they are not very good. I've heard nothing but bad things about them (from clients of theirs that have come to us to fix their dogs) so that's what I think of when I hear that name.

As for the risk of offending people... well if it offends them they don't have to use you. It's as simple as that. You can't please everyone all the time.