What do you do when someone takes over your phone and gets into your Apple account? How do I change my password?

You might want to consider changing your password and making sure it is a strong one. You can also add 2 Factor Authentication to your account for more security. If the attempts continue, you might want to consider a name change.

Link to contact Apple Support in the article.

Apple ID has been compromised.      

Security and your Apple ID.      

 Apple ID Password Change.     

Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

Apple ID -Two-factor authentication          

Two Factor Authentification availability.    

2 Factor Authentication - How to generate a recovery key

Apple ID - Using app-specific passwords.     

Apple ID - Two Step Verifications FAQ