Star Trek: 10 Secrets Of The USS Stargazer

First appearing in Star Trek: Picard's second season opener, appropriately titled "The Star Gazer", the Sagan-class Stargazer is referred to by Admiral Jean-Luc Picard himself as a "refit". According to season two and three showrunner Terry Matalas, there are at least some components of the old Stargazer incorporated into the new vessel, making Picard's statement technically true:

Like the TMP Enterprise, it’s a massively updated refit. I like to think of it as the story of the broom: If one day you replace the handle, and another day the brush, is it still the same broom? We thought of it as a vessel endlessly repaired and upgraded, brought in-line with current-future tech, so that somewhere underneath all the lights and polish are the bones of Picard’s original ship. Does it make sense? I don’t know. But I sure like the spirit of it.

Whether it makes sense or not, the producers still felt the Stargazer was a minor vessel in Starfleet's pantheon of starships. According to production designer Dave Blass, he personally decided not to grace the ship's registry with an "A":

I dropped the hammer on this one. The Stargazer is an important ship, but it does not hold the status in the Federation that the Enterprise had. I didn’t feel it was warranted. Because then every ship gets it and it becomes a thing. The Stargazer didn’t have that legacy.