The fake Horcrux was a locket, and while it was designed to look like a real Horcrux, it didn't have any markings or initials on it.
The real Horcrux locket, belonging to Salazar Slytherin, did have the initials "R.A.B." engraved on it, which stood for Regulus Arcturus Black. However, these initials were only present on the real Horcrux, not the fake one.