Hello
Do you want to close out the entire Microsoft account, or do you want to keep the account, but remove hotmail.com as username and give it a different username?
If you want to close the entire account, use this instruction: https://support.microsoft.com/en-us/account-billing/how-to-close-your-microsoft-account-c1b2d13f-4de6-6e1b-4a31-d9d668849979
If you just want to give it a different alias/username, Go to https://account.live.com. go to Your Info > Sign in preference, Add an alias.
You have two options here:
Create new: this will allow you to use the native domain outlook.com to create a new alias.
Add existing: this will allow you to add a 3rd party email address, such as yahoo, gmail, as long as they are not already associated with another Microsoft account.
Once added, make this new alias your primary alias, then you can delete the other email as alias, and that email is free from this Microsoft account instantly.