How to change my "sender name" that people receive with my e-mail.

I have a Mac Mini using "Mail" 8.2. When people receive an e-mail from me the name that appears in their in- box is not the one I want displayed. When I go to Mail, then preferences, the box for "full name" is the one I want but it's not the one displayed to the people who receive the e-mail. Does anyone know how to fix it?

Thanks

Ralph