It's not exactly clear from your post but it seems that you may confusing your workgroup name with your connection name. If both computers are running Windows 7, then right click computer, choose properties and look in the area labeled "Computer name, domain, and workgroup settings. Click the link that says "Change settings" then the button that says "Change" in the box labeled "Workgroup:" enter the name of your choice on both machines, make sure it is the same name.
The actual network connection name has no particular impact in so far as networking is concerned, but for the sake of clarity you may want to change that also. Type ncpa.cpl into the search box and hit enter. Select the specific network connection you wish to change then right click and choose rename. You may want to name them something simple like "Wired" or "Wireless" but again this doesn't having any affect on the actual networking of the two machines.
Open the network and sharing center and in the left column choose "Change advanced sharing settings" make sure you have "Turn on network discovery" and "Turn on file and printer sharing" selected. The rest of the settings are a matter of personal preference depending on how and what you want to accomplish.