Someone is using my Apple ID out of state. How would I handle this situation?

If this is an e-mail you received, or a popup on the screen, about the time you were actually logging in, there is probably nothing to worry about. The location in the e-mail is where your ISP reported it. If their servers are in a location distant from you, there will be a large error.

If that isn't the case, the e-mail may be a scam, especially if there is a link for you to click. If your question isn't answered, please provide more information.

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.

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.

You can manage devices on the account by logging in to appleid.apple.com.

Great Resource:

Check your Apple ID device list to see where you're signed in:

https://support.apple.com/en-us/HT205064

You can change your password to secure the account and set up two-factor authentication if your concerned about potential outside access.

Passwords been changed 10 times’. Completely hack