Maybe a bit more context. The plan is for the 3 of us to have kids, so both of them will be having kids with me. Not sure if that matters or not.
I guess with the "new" woman in the relationship (new being about 9 months in) and a newborn already here it may be best just to wait a little on what to say she is to the child until she has her own children (and hence fully committed to the family).
I guess one reason people prefer using their real name is it is easier to leave the relationship compared to if they called you dad or mum. If this "New" relationship doesn't last and we have been letting the children call her "mum" then they have lost a "mum" instead of "jane".
Still, with friends calling themselves "aunts" or "uncles" to our child I feel like if there was a special word for "mum #2" it would ensure they are "different" than most people in name as well as function.