NCC-1718 was the registry number of a Federation starship that was in service to Starfleet in the mid-23rd century. This unnamed starship underwent a layover at Starbase 11. The ship's number was seen on a chart indicating the repair status of several vessels. (TOS: "Court Martial")
Unfortunately, we don't know what this ship was named since it was only identified by its hull number. The NCC-1718 registry was assigned to USS Endeavour in Greg Jein's registry list from The Case of Jonathan Doe Starship. That ship was actually mentioned in an early 1967 draft shooting script for TOS: "Amok Time",  and concurrently included in internal memos from D.C. Fontana and Robert Justman, suggesting lists of possible Constitution-class starship names to consider for use in The Original Series. These lists, published in The Making of Star Trek (pp. 164-165), were used to match Endeavour with the registry NCC-1718 that appeared on the wall chart seen in "Court Martial" by Jein in his article, though the ship had not made the cut eventually.
When Endeavour was reintroduced into the franchise a quarter of a century later, Mike Okuda had however, a different number (NCC-1895) assigned to Endeavour in a graphic in Star Trek VI: The Undiscovered Country, leaving the "NCC-1718" registry orphaned.