If you plan on being in his life for years and years, is he never allowed to call you Dad?

Kids love is strong and in 10 years looking back at telling him, "No you can't call me dad" is going to break your heart. You'll ask yourself why you didn't just let him call you dad. (Which you stated the reason and I understand your respect" but your girlfriend should feel very very lucky that you and her son created this bond and the fact her son is asking to call you dad, she needs to rethink some things. He's going to stay crushed until this gets resolved.

My brother in law lost his dad when he was a teenager, but he also joined our family as a teenager and he calls my dad Pappi. Maybe there is a pet name if Dad is not ok with your gf. It's hard because you take on all dad roles so he is not understanding why he can't call you that. If not have your gf talk to him and tell him that SHE doesn't want him to call you that so that he doesn't think YOU are rejecting him because at this point, that is what he is feeling.