The name is there by default so with your setting you should be seeing
Your Name Your Email Your Subject Your Message
On the contact form page.
Do you have all those fields?
Are you asking about the name not showing in the actual email itself? If this is your questions you need to nook at the header details and there should be a "reply to" and that will have the name & email address. The main name that show as sender is the automated from site so you know it's from your site.
Unfortunately many users are not as tech savvy, so if I need to create a gpEasy site and hand it over to my client it'll be tough/cumbersome/difficult for them to remember and use these steps to extract the person's name and email address from the header if they want to create a database out of the people responding to them through the website. Wouldn't it be easier if the info was part of the email content as well?
I guess it all depends on what you are trying to do with the names and email addresses. At this point I think gpEasy is designed for simple use scenarios, thus tying into a database I don't think is something the developers are going for at this point.
As it stands, a person using something like gmail would have no problem having the emails added to their contacts automatically; however, the names may need some adjustments but I haven't really looked at it as I'm not in that situation. If you perform some testing on gpEasy and the contact form and see a legitimate need for a feature that fits with the gpEasy easy to use philosophy don't be afraid to submit a feature request--see the contact page in the sidebar ;)