Formal:
* Ma mère s'appelle... (This is the most common and neutral way to say it)
Informal:
* Maman s'appelle... (This is more familiar and used with close friends and family)
Other possibilities:
* Je m'appelle... et ma mère s'appelle... (This is a more complete way to introduce yourself and your mother)
* La mère de [your name] s'appelle... (This is more formal and impersonal)
Example:
* Ma mère s'appelle Marie. (My mother is called Marie.)
* Maman s'appelle Sophie. (My mom is called Sophie.)
* Je m'appelle Pierre et ma mère s'appelle Anne. (My name is Pierre and my mother is called Anne.)
Choose the option that best suits your situation!