I quite like it. I like Bruce and Bruno and Gus too which no doubt somebody will say woof woof.
If Barnaby gets the mumsnet approval then I don't see the difference tbh.
Felix is lovely but it's at least as cat as Rex is dog.
My name can be a dog's name. Well I suppose any name can be. But once a friend's mum said "are you hungry maggie?" I said "oh, er, a little peckish thank you mrs patterson". I was talking to the dog she said.