If you have changed you password, you should be safe. You might want to consider a name change if you entered your Apple ID to 'hide' the ID.
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 will always address you by your name or the name they have on file for you and the e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more.
Avoid phishing emails, fake ‘virus‘ alerts, phony support calls, and other scams
Identifying legitimate emails from the iTunes Store
Send the e-mail to Apple as an attachment to a new e-mail before deleting it. You can forward as an attachment by going to Mail/Message/Forward as attachment.