It is correct that you can change the name or number on the files. It could be reset each time or reset by the camera but the shutter count shown in this site should be correct.
My picture I just checked showed a number of 53 but the shutter could is 243. The 190 extra are probably the ones from when they were refurbishing the camera at Nikon or it possibly was a return or demo camera that had only a few clicks on it.