Vita + amine, actually. Amines are compounds with an NH₂ group; amino acids are a subset of that.

The person who coined the term thought he had isolated an amine that was effective against a certain disease. What he had actually isolated was neither an amine nor effective against that disease but was actually a different essential compound. (He was looking for what we now know as thiamine but had actually discovered niacin.)

The name “vitamin” stuck around despite the fact that most vitamins aren’t amines.