I interpreted it that the Messrs put their names on the front of this ancient artefact. From Chapter 25:

And the Weasley twins weren't about to turn the Map over to Dumbledore. It would have been an unforgivable insult to the Marauders - the four unknowns who'd managed to steal part of the Hogwarts security system, something probably forged by Salazar Slytherin himself, and twist it into a tool for student pranking.

By the way, this reminds me that the Twins seem to have found a couple of errors on the map:

"Intermittent one fixed itself again. Other one's same as ever."

(That's why they might have shown it to Dumbledore, to get it fixed.) In canon, there are important (and only apparent) errors on the map in Book 3, showing Peter Pettigrew and Bartemius Crouch. What are they showing now?