Apple id

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.

Security and your Apple ID.      

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 Verifications FAQ    

Hello,

• Due to the urgency of this situation I would strongly suggest following all steps in this guide (If you think your Apple ID has been compromised - Apple Support). 
• Then I would suggest reading all of this guide to make sure this doesn’t happen again (Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support)

Drake