* Mes parents s'appellent... (formal) - This literally means "My parents are called..."
* Mon père s'appelle... et ma mère s'appelle... (formal) - This means "My father is called... and my mother is called..."
For example, you could say:
* Mes parents s'appellent Jean et Marie. (My parents are called Jean and Marie.)
* Mon père s'appelle Pierre et ma mère s'appelle Sophie. (My father is called Pierre and my mother is called Sophie.)
You can also use the more informal papa and maman instead of père and mère, especially when speaking to friends or family.
* Mon papa s'appelle... et ma maman s'appelle...