My husband walks 6 Chihuahuas and carries Bella the Yorkie. He practically glows when he does it and he is a very macho heavy equipment mechanic. He always says that he is very confident in his sexuality so he doesn't need to prove it! I think the real reason is that ladies pay attention to men who have precious dogs!
Tell your man that and he may be more easily persuaded to call her anything you like.
PS. I like SOPHIE