What is the side fin on a fish called?
If it’s up toward the head, it is probably the pectoral. If it is back near (but not at) the tail, it is probably the pelvic.
Here is a Basic Fish Anatomy Glossary to check out. Fish bodies can take an amazing variety of shapes, so the pectorals and pelvic may not appear where you might expect to find the “chest” and “pelvis”.
If some fish have an additional lateral fin, you’ll need the help of someone more familiar with ichthyology than I am.
This all sounds fairly fishy to me.
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Alomst any fin on the side of a fish will be the pectoral fin. On the more primitive fish (like sharks) these are lower on the sides; alomst on the bottom. More advanced boney fish tend to have them right up on the sides.
The fins up near the front are, as mentioned by tomndebb, the pectoral fins. If the fish in question has only two pairs of fins (non-dorsal, of course), then the rear-most pair will be the pelvic fins. If the fish in question has three pairs, then the middle pair will be the pelvic and the rear-most will be the anal fins (for, I trust, obvious reasons).