If you bring up the contact number, and select EDIT, you should be able to enter additional information such as company, e-mail, notes, etc. Sometimes, on some phones, when in the edit section, you have to hit menu, and get more settings where you can add things to the contact.
Bear in mind options vary between phone models,
Also note, this info will not display when a person calls "caller ID" Only first and last name.
As a Workaround, I usually include the company name in the Name field along with first name or after the last name. For example "Bob Microsoft" Chances are, I only know 1 Bob at microsoft. If space permits, you can add Microsoft after the last name in the same field. In this case, it would display Bob Smith Microsoft" when he calls.