I have a fatboy. Good fin has everything you need, wide base for drive of the bottom, lots of tip area for walking nose ward and the cutaway helps them turn a bit sharper.
Mine was a bit small for the 10ft log so I got the fin next to it in the photo below. It's a jai lee fin from captain.
Much better on the log bit more area and hold.
It's 10.25" and is kinda between a D fin and a dolphin. I'd actually like it a touch bigger.
7.5 is to small.
Dolphin fins are a good place to start the suit most boards in most waves.