I want to move out of my mother house and go to my grandparent's house. Is that possible me, being 13 years old?

My mother constantly calls me by the name I don't identify with, and uses the incorrect pronouns when referring to me. Not only that but she calls me names, and makes me feel like the absolute scum of the earth. My grandparents are the ones who raised me and I have learned everything from them. They're what I would actually call my parents cause that's what they are to me.