
"If"... it was bitten off, and bitten off at the hard spine (bone) it is not usually able to grow back, of... bitten off on the soft rays of the fin, it is possible to grow back.
I have had many fish where the spine of the fin is broken or bitten off, and it is impossible to grow back
Note the split in the caudal of this Paratilapia, it never closed and I had it for years.

As others have said, it can be mostly cosmetic, and unless the fish has trouble with balance, it shouldn't matter to its general quality of life.
If a defect, it should have been culled, but these defects are often not noticed in a crowd of fry or juvies, just as you didn't see it until you got it home.