I think it's great. I really liked it for DS2, but it was too close to DS1's name (one syllable with an e in the middle). It's true that it's historically a stereotypical dog's name, but then Felix is a stereotypical cat's name and I know loads of boys called Felix, as well as a few called Rex. It isn't like calling your child Fido - Rex is a human name used on a dog, just like Felix is a human name used on a cat. And I've never actually known a dog called Rex or a cat called Felix, though I know loads of dogs and cats called Finn, Ben, Max, Poppy, Molly, Daisy, Oscar etc (and I also know loads of children and adults called all those names).
Anyway, people call their children Otis which is the name of a famous lift brand and Noah which is the name of guy with an ark. Everything has a precedent.