I'd expect to find it under the realm of ‘Tools’, ‘Options’, ‘Preferences’ or such.
Check your help file too, it may explain the process.
Or try a web search with the name of you e-mail program and the term “display full name”. That ought to get you int he right direction.
Feel free to e-mail me at my personal address and I'll tell you if it worked.
I was able to change it on my daughter’s account so I know how it’s supposed to work, but it won’t let me change mine. We both use Outlook Express.