When your mom is in a relaxed mood, speak to her about the name-calling and how it's hurting the relationship. Ask her to stop. In the future, if she starts up again, leave the room immediately. Moreover, never get in the mud with her.
We teach people how to treat us. By disengaging from the situation, you'll be informing her that this behavior is unacceptable. If she wants a relationship with you, she must treat you with respect.
Name-calling is typically a symptom of a bigger problem. If this behavior has only shown itself recently, your mom may be stressed out, depressed, or angry, and in need of therapeutic intervention. Ask her if there's anything you can do to help. If the name-calling has always been a part of her behavior, that indicates low character. She's unlikely to change so it's best to distance yourself from her.
It's said that the person who causes us the most emotional pain is our greatest teacher. Take what you're learning from your mother's name-calling and make yourself a better, kinder, and stronger person. Vow to never use words as weapons to hurt others. Realize how powerful they are and speak them to lift people up, not tear them down.