...when his actual father is still a regular feature in his life?
I've been mulling this over for a few days and honestly don't know whether IABU and judgy or not. So...over to you lot!
My ds had a friend (let's call him J) round the other evening. J lives with his mum and mum's partner since she left his dad about 3 years ago. I don't know the dp very well, seems alright and appears to have a good relationship with J. However, I know that J also sees his dad regularly, goes on holiday with him, spends school breaks etc with him, so they have a close relationship too. All good, in fact.
So, it gets to pick-up time and J looks out the window and says 'my dad's here'. I go to the door and am a bit surprised to see the dp standing there. Obviously I don't say anything! But I was just 
I could understand it in some situations but J was not little when his parents split, it's not like he's never known his dad as his dad iykwim? To add a bit of context, I am divorced from ds's dad, it wasn't an amicable split, I have a dp with a very good relationship with my ds, but I would never, ever let ds call my dp 'Dad' because no matter how much of a twonk I think his dad is, he's still his dad. And equally, I'd be gutted (and furious) if exh encouraged ds to call another woman 'mum'!
So, AIBU to think this is a bit...well...wrong?