I'm on both sides of the fence. I do not think I would appreciate my young children calling someone else mom. As adults, it is up to them to decide how it will be. On the other side of the coin, I have a step daughter that I have raised since she was 10 and she is now 21. We had full custody. She calls me by my first name to my face but refers to me as her mom or step mom depending on the situation.