Apple ID being used

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.     

 Apple ID - Using app-specific passwords.     

Apple ID - Two Step Verifications FAQ    

Assuming you are using two-factor authentication,Check your Apple ID device list (https://support.apple.com/en-us/HT205064) and remove any device that shouldn't be signed in using the steps in the link.

If there are none that shouldn’t be signed in, then you should not have a related problem at this point. But, if an unauthorized device signed in, do what Eric Root suggested about changing your password.