Why would the class name change with a refit? We have no evidence of other ships getting a new class name when they got refit. For that matter, why would the ship get its registry number changed just because it was refit.
Besides, the dialogue is very sloppy on the matter. The Titan is described as "still having that new ship smell" despite the fact that Shaw is stated to have been commanding it for five years, and that its engines are twenty years old.
Then things get really weird given Matalas apparently told Todd Stashwick the Titan A was launched in 2402, leading Stashwick to get
this t-shirt made for himself. Never mind the fact that a launch date in 2402 is a very interesting trick for a season set in the year 2401, such a "recent" launch date would also seem to contradict the dialogue given in the show seemingly stating Shaw took over command of the Titan from Riker.
Bottom line, the writing in Picard S3 is a damn mess and its best not to take anything stated in that season at face value. I know, Trek fans are all about mindlessly adhering to Canon and the Words Spoken Onscreen, but maybe in this instance think the matter through and contextualize it to see if it even makes sense before trying to build an argument around it.