My partner has a 5YO daughter and i have been in her life since she was 3, i dont have a 'title' she just calls me Amy. Although if she's playing with my neice she calls me Aunty Amy as my niece does and she idolises her so copies most of what she says haha.

Some people who dont really know our situation sometimes say 'go and ask mum' or something along those lines and its too long a story to explain so i just smile and nod. Most of the time she corrects them tho

Im a bit confused on what you mean by what should she be introduced as? Cant you just say this is M? Are you talking about to the kids or to other people? If the kids already know her id just continue calling her what they do now?

As heavenly said, i do the same, i call my Step mum by her name