It is good to hear from you. I have always heard that the cemetery was called "Guilliam Barker Cemetery". Guilliam and his wife, Sarah along with some of their children are buried there. Very few of the graves have markers, and a lot of them are unreadable. I think that since Guilliam and Sarah's tombstone could be read that this is how it came to be named "Guilliam Barker Cemetery". I think that this cemetery may be the original "Old Barker Family Cemetery". Not far from this cemetery is a place where Mary Susan "Curtie" Barker is buried, this has been called "Barker Cemetery". Also not far away is where James Madison Barker and family are buried Then nearby is where Daniel Barker and family are buried. All the land where the cemeteries are located was once owned by Joseph Barker and his brother, Allen and descendants. To help locate the cemeteries they started being called by the name of whoever owned the property and is buried there. If they were all called Barker Cemetery then it would be hard to locate a particular grave.
Hope this helps.