I do not know that I buy this as a reason for him being named this, but here's how I would answer this question:
If you think about Captain Beatty, he is anything but happy. He is clearly conflicted between what his job demands of him and what he really wants to be like. He is so conflicted that he ends up pushing Montag into killing him with the flamethrower. This is clearly not a happy person and so it would be pretty ironic to name him after joy or happiness.
I believe that Beatty is unhappy because he secretly loves books and thinking. To me, the proof comes in how well he knows books. He can quote from all kinds of books and he even understood the old woman's quote about "play the man, Master Ridley" which seems pretty obscure. I don't believe he would have memorized all that stuff if he didn't love it and agree with it.