Here's a fan theory about inconsistent starship registries, one which I'm sure other people have had before but that I think there's some firmer evidence than just speculation in a particular starships case. That ship is the USS Hood, Excelsior class starship. In the 1st Season of TNG, she was labled NCC-2541, and when her registry was next seen in TNG season 4 on a chart, she was listed as NCC-42296. The chart claims she is undergoing a "major systems upgrade", at Starbase 134. I submit that this "major systems upgrade" in fact explains the change in registry of the USS Hood, and that she was originally the NCC-2541 but reregistered under a different registry number as a result of her upgrade.
Logically, I think this makes sense, and if extrapolated it set president for the USS Saratoga of Star Trek IV (NCC-1887) being the same as the Saratoga destroyed at Wolf 359 (NCC-31911). I imagine that the producers, or art department intended that to be the case, otherwise why not use another model (Nebula, Excelsior, ect ect) to represent the Sara? No doubt it to me it was meant as a tip of the hat to the film. There's no reason to think it isn't the same ship, just with a new registry that reflects it's modifications.
Logically, I think this makes sense, and if extrapolated it set president for the USS Saratoga of Star Trek IV (NCC-1887) being the same as the Saratoga destroyed at Wolf 359 (NCC-31911). I imagine that the producers, or art department intended that to be the case, otherwise why not use another model (Nebula, Excelsior, ect ect) to represent the Sara? No doubt it to me it was meant as a tip of the hat to the film. There's no reason to think it isn't the same ship, just with a new registry that reflects it's modifications.