Why are amino acids named amino acids?
When learning about amino acids, the primary things that were pointed out were that they had an amino group and a carboxyl group...
Why amino acid? Not carboxyl acid, or some mix of the two, or something else?

You stated why it is called an amino acid, the name comes from the amine (amino) and the carboxylic acid (carboxyl group).
Amines are weak bases, so the acid portion of the name must come from the carboxylic acid.