Griffins are also dogs, aren't they? Little pooches with long legs and squashed faces? I'm sure my mother had friends who bred them.
As for a child hating being named after a monster - I've never met one who wouldn't be delighted! And I've met plenty. Anyway, griffins were good-guy monsters who guarded hoards of gold! And then there's the whole
Harry Potter Griffindor connection, when he's old enough. I rather like it! But if your in-laws prove intractable, might they and your husband perhaps consider
Griffith?