(covers information from an alternate timeline)
The USS Pasteur (NCC-58925) was a 24th century Federation Olympic-class starship operated by Starfleet Medical, as indicated by its emblems on the primary hull and their prominent presence on the bridge. The Pasteur was constructed by the Skywalker Division at the Marin County Starfleet Yards.
In an unknown, alternate future timeframe, this medical ship was commanded by Captain Beverly Picard. The ship was destroyed by two Klingon attack cruisers after the Pasteur crossed the Klingon border to scan the Devron system for a temporal anomaly. However, the survivors of the attack were rescued beforehand by the USS Enterprise-D, under the command of Admiral William T. Riker. Among the Pasteur's crew of that timeline was Ensign Nell Chilton, who died during the Klingon attack. (TNG: "All Good Things...")
According to the Star Trek Encyclopedia, Journey's End: The Saga of Star Trek: The Next Generation, and an interview with Michael Okuda on the TNG Season 7 DVD special feature "The Making of 'All Good Things...'", an early pre-production version of the ship's dedication plaque designated the vessel as belonging to the "Hope-class" starship, before being changed to Olympic-class. It would also, however, erroneously list the ship's registry as NCC-58928.