We got our GOH badges a couple of years ago. We got them at Pooh's Corner in DTD but have heard they are no longer offered except with standard names...no custom spelling or unusual names and maybe only certain names on certain character/color badges.
You can try Mickey's Star Traders in Tomorrowland and at the Emporium in MK, and at Hollywood 5&10 in MGM. I'm not sure where they are offered in Epcot or AK.
I once read on the Dis that they were changing machines to do the engraving but hadn't installed them at that time. You may be able to get custom badges at the parks but I don't know.