Here's what we do(my husband is my son's step dad)
I told David he has 1 and only 1 dad(my ex)Kevin is his step father and if doesn't want to call him dad than that's fine.David calls Kevin by his name but will introduce him as his step-dad Kevin.
Just like now my ex husband is getting remarried he told her that she'll never be his mom because he has only 1 mom,she will be his step-parent and he won't call her mom....
Now in your case i would say don't fight it.I say talk to his mom(Judy)about it.Say that you never pushed it but this is what your son has picked to call you and he knows that you are his mommy but if he wants to call me(fill in the blank)than that's fine but i'll reassure him that you are his mom
Sorry no real help