Someone's trying to sign into my Apple ID account

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.      

 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    

Perhaps these articles will help;

If you think your Apple ID has been compromised - Apple Support

Report a security or privacy vulnerability - Apple Support