What kind of email software are you using?
For instance, for RoundCube, which is a form of Webmail (meaning you check your email via a web browser), you would just need to enter the email address and name into your email address book. Then, when you start to type the name, RoundCube would check every name in your address book to look for matching names to suggest.
The same thing may work with whatever type of email software you are using - webmail or not - but it does vary, so there may be other changes you need to make.
