What are numbers that are not prime called?

There are many different sets of numbers. Assuming you mean only the positive integers and purely the 2 states prime or non-prime, the ones that are not primes are termed composites. One caveat, the number 1 is somewhat unique, being considered neither prime nor composite.

[ However, relaxing this, other numbers like the set of irrationals and reals are mostly not prime as well. This would be numbers like the famous Pi or a number like 2.17]
Composite is a number that is not prime.