How do I change the name that appears alongside my email address??

How do I change the name that appears alongside my email address??

I have just set up an email account using my own URL and I can both send and receive email OK. However, when I send an email to someone, it appears in their inbox with a sender name that I don't want. (For some reason it's using the username from my Hotmail account?? I entered this when I initially signed up). How do I change this? I would rather it came up with my domain name/ I.e. company name in people's inboxes. Help! :)