Can I use the program on two Macs with one registration code?

Yes, if you are using a registration code of Family License. 

FonePaw MacMaster is offered in three versions to fit different needs.
 
Lifetime Family License - A registration code of a family license can be registered in 2 to 5 Macs.
Lifetime Single License - The registration code of a single license can be only used on one Mac. Once the code has been registered in a Mac, it cannot be used in another Mac.
One-year License - The registration code of a one-year license can also be used for only one Mac. The code is invalid if trying to register on another Mac.
 
If you have two or more Macs that need MacMaster, Family License is a more reasonable option for you.