Managing personal Outlook.com account settings, security, and privacy
Greetings!
This is Tin, sorry to hear that your account has been hacked. I understand that you would like to close or delete that account instead. Regarding this, in order to close an account, you need to have an access with it first. Please try to recover it using the MS Account Recovery Form: http://account.live.com/acsr
If it didn't help, it would be best to reach MS Accounts & Billing Support to check options. Please be informed that you need to be signed in in order to reach them, since your account has been hacked, please use any MS Account that you have access with.
Kindly open this link: https://support.microsoft.com/contactus/
Please choose Account / Security / Recovery and please select support agent or chat.
Please try to reach the MS Account Support from there.
Thank you,
Christine L