Someone broke into my Apple ID

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

 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

 Apple ID - Using app-specific passwords

Apple ID - Two Step Verification App Specific Passwords

Apple ID - Two Step Verifications FAQ