Hi Beth,
It's not hard for someone to change the name associated with an email address.
Please double check that the real name in your Hotmail account settings is correct.
The problem could be that someone has your name in their settings in a mail program on their computer such as Mozilla Thunderbird or Windows Live Mail.
Also, double check your contacts list for an entry related to the real name & email address mismatch.
It's not clear exactly where you're seeing the problem but I suspect checking all of the above will help you fix the problem.