Meine Mutter ist Maria.
Is it correct to introduce someone like that? Or is it wrong, and the only accepted form is the following?
Meine Mutter heißt Maria.
Meine Mutter ist Maria.
Is it correct to introduce someone like that? Or is it wrong, and the only accepted form is the following?
Meine Mutter heißt Maria.
If she is present, I would use a gesture to make clear who I am talking about and say
Das ist meine Mutter Maria.
As for when she is not present, it depends a lot on what you want to say.
Meine Mutter heißt Maria.
Would be used, if someone asked you what her name was. Using "ist" in this context is a bit unusual, but probably not completely wrong.
Meine Mutter ist Maria.
Is a lot more general, and could eg be used when there is a choice between 5 different people who are not present, and you are asked who of those is your mother.
I guess the general rule of thumb is, that when you are talking about the name, "heißen" is the word of choice, if you are talking about the person, you would use "ist".
No, as a way of introducing your mother this is not correct in either standard or colloquial German.
You have or hold a name but you are not your name.
Maria sein sounds like Papst sein or krank sein. It sounds as if you implied that she holds a ‘Maria-position’ or a role in a play:
Meine Mutter ist Maria, Peter ist Josef und ich ein Hirte. Den Ochsen suchen wir noch …
This is fine, but not introducing us to the persons but to the roles they have in a play.
One could say Maria ist meine Mutter, but not as an introduction, only as clarification.
For an introduction choose any of Gerhards two suggestions or, best also with some gesture: Meine Mutter, Maria.
A rather colloquial version would be Meine Mutter ist die Maria.
Meine Mutter ist Maria would be correct if you are introducing yourself to someone who knows your mother.