My oldest calls me mummy. It's was his choice, we used my name and he chose otherwise.
He was 2.5 when I met him (I had been dating his dad for six months prior to meeting him as I did not want to pop into his life until I was pretty sure we could make it work) and at about 3 he clambered onto my lap, looked me in the eye and said: "you're my mummy, aren't you?". I said that his BM was his mummy, but I do the same things as a mummy for him. He I was 4-5months pregnant at the time and when he persisted in wanting to call me mummy we let him, as he would get distraught when other members of DHs family told him otherwise. He has me and as he's got older he knows that he was in his other mummy's tummy not mine but that doesn't change that I love him.
I've always defended his choice. Maybe it's selfish, but if he decided he knows he is free to call me by my name if he preferred. I will not however, force him to use my name or another name when I let my other son, my birth son, call me mummy.
Looking on here I've questioned it a bit, theres a lot here who seem to say i am not his mother and never will be, but it feels right in hindsight for us as a family. Maybe if we did not have full residency it would be different. But his other mother is in his life for three hours a month, doesn't phone for him (we used to run a separate mobile phone for him until we realised we'd paid for a mobile for four years which never rang once) and doesn't look for more contact. I have never and would never say it out loud where he could possibly be nearby to hear, but I know who his mother is. And I think he does too. That's why I wouldn't force him to change.
Sorry for the long post and if this thread is too old to resurrect. New here. :)