I believe I have a male and female because I have seen them mate. How do I determine the name of this crayfish? And am I correct that I have a male and female?
Keep them separate except for mating. They are quite agressive and will eat one another when one molts. Put them together only for mating.
When the male molts, wait a week then put them together in a bucket 1/3 full of water. If the male is in the right phase they will mate. If they don't mate almost imediately, separate them again and wait for the next molt.
If you've seen them mate, you will likely get some eggs. Keep track of the male's molts as he is only sexually active every other molt.