It's called "Yakety Sax" if you're trying to source it for an alternative take.
As someone who's not a "real" diver, although I stick a fin in the water now and again so let's say 1/2 diver... I actually really like the (very few) videos out there where there is just the original sound, although if for example a GoPro is in a waterproof case, not sure how that's recorded? The sound of the second stage, an occasional bottle clunk, if dive scooters are used (not so much UK sumps

but in mines) they make nice whirring noises. It all gives it an underwater feel, rather than music which seems to make it feel less underwater for me.
For me anyway, it gives an extra dimension I love. My first ever dive (doing an open water with a bit of a cowboy outfit abroad, zero pool sessions after you watched the PADI online training then you were given kit and sent to the harbour) I was mesmerised by the different sounds, boats that make deep marine diesel engine noises on surface, making strange whining/whirring noises as they passed nearby. The noise of breathing. I love hearing those underwater sounds.
Anyway I'd put original sound in first place for soundtrack, even better than Yakety Sax!
Enjoyed the video, thanks!