I have a document that was created by someone that left the company so his name no longer appears in the pick list. (I assume this is fed from Active Directory). Is there a way to enter a name that is not on the pick list?
No you cannot.
When you type the first three characters of a user name, group name, or claim (such as an e-mail address) into the text box, People Picker automatically searches for results that match the first three typed characters from the source you have configured. So if the name you have typed is not in your source(AD or other source), then you cant have that value in the people picker. It is by design.