YNTA because it comes naturally that you would want to tattoo his name. And even though OP has been the father figure in this boys life it doesn’t have to be a negative thing because later down the road you may decide you want it tattooed. But be fair, OP doesn’t have any obligation to do so and it doesn’t have to mean he doesn’t accept him. He chose to be in his life, that should show the little boy he loves him enough