I am moving to Arizona, I currently have a commercial cleaning business in nj can I transfer this license to Arizona

Licensing is done by each state individually. And no, you could not just transfer this license there you would have to get an entirely new license in AZ once you move there. You may also need to get business insurance coverage in AZ if your present carrier does not cover AZ locations. Check with your current agent to see if you will need new biz insurance once you move there. Most carriers are only licensed in one state and some are licensed in all states. Best to check this out before you find out you are not covered.