Star Trek is much more than just the USS Enterprise with the Starfleet's current ship count being estimated at somewhere between 5,000 to 10,000 ships. Some of these ships are named in honor of mythological figures such as the USS Chimera, the USS Agamemnon, and the USS Apollo. As is common knowledge, Apollo is also the designated name of NASA's many Moon programs. Similarly, other NASA initiatives such as Challenger, Colombia, and Endeavor also get commemorated as Starfleet spaceships in the Star Trek franchise. Another common naming method for these planet-traveling vehicles is incorporating actual characters from the canon and even real-life personalities.
So, with every USS Chekov and USS Sulu, dedicated Trekkers can also find cool Star Trek spaceships named after visionaries like Albert Einstein, Mahatma Gandhi, Neil Armstrong, and many more. So far only six ships have been identified in the canon to have been named after Star Trek characters. And when it comes to their etymology being linked to real-life personalities, only one ship has been named after a Star Trek actor. But given that the universe of Star Trek continues to be explored and not every spaceship has been identified yet, there's a good chance the franchise will come across more ships christened after some fan-favorite characters.
Archer
Captain (later Admiral) Jonathan Archer's contributions are wide-ranging, including expanding United Earth's influence in the Alpha and Beta Quadrants of Star Trek's Milky Way galaxy along with building first contact with species like the Klingons and Andorians. There have been three starships named after the Star Trek: Enterprise protagonist. The first USS Archer debuted in the movie Star Trek: Nemesis as a part of the Starfleet’s Omega Battle Group in 2379. The series premiere of Strange New Worlds introduced a USS Archer from 2259, whose three-member crew was abducted by the Kiley and later had to be rescued by the Enterprise.
There is evidence to support that the Archer-type starships were still in use up to the 25th century. The Picard episode “Farewell” briefly featured an Archer joining a Starfleet armada that is coordinated by the Borg Collective ship Singularity. The intention of the armada was to deflect an energy burst from a transwarp corridor. While it features briefly in Picard, this version of the USS Archer is different from its previous two appearances as this one was a Ross-class ship. The Starfleet began using Ross spaceships from 2401 onwards with most of these ships bearing a resemblance to the earlier Galaxy-class but displaying technology from more recent designs.
Chekov
A 24th-century Starfleet ship, USS Chekov mainly appeared in Star Trek: The Next Generation, seen in action but also shown fying to its own destruction. Joining an armada of 40 ships, Chekov was assigned to intercept the artifact Borg cube that was on its way to Sector 001. The ship’s crew valiantly encountered the Borg vessel, but the entire human fleet was wiped out in the ensuing battle. While some viewers might think it is named after Russian writer Anton Chekov (like the USS Tolstoy, which takes after Leo Tolstoy), the ship is obviously a nod to The Original Series alumnus and USS Enterprise navigator Pavel Chekov.
Hikaru Sulu
The USS Hikaru Sulu has been in service since the early 25th century, first introduced in the season 2 premiere of Picard. Mentioned only in dialogue, not much is known about the Federation Starfleet property except that it was assigned to Starfleet Cadet Br'ionn Raul. The ship's name is derived from the Star Trek: The Original Series and Star Trek movies alumnus Hikari Sulu, an iconic Starfleet officer famously played by George Takei. Even though Sulu began working in the sciences division of the USS Enterprise, he later piloted the USS Enterprise-A and eventually served as the Commanding officer of the USS Excelsior.
Janeway
Named after USS Dauntless Commanding officer Kathyrn Janeway, the USS Janeway appears in Star Trek: Discovery as one of three ships investigating the Dark Matter Anomaly that had appeared in the galaxy’s Venari sector in 3190. Along with the NSS T’Pau and an unnamed Starfleet ship, Janeway was tasked with monitoring the gravitational anomaly. All these ships, unfortunately, disappeared mysteriously as they approached the anomaly. The ship’s namesake continues to be integral to the franchise, first introduced as the captain of the USS Voyager, the Star Trek: Voyager character returned to the franchise with the animated "stealth" sequel Star Trek: Prodigy.
Cochrane
The inventor of the warp drive and the first human to travel faster than light, 21st-century scientist Zefram Cochrane is an eccentric genius who has appeared in several Star Trek properties including The Original Series, First Contact, Enterprise, and Lower Decks. He lends his name to the Oberth-class starship USS Cochrane, which has been active since the late 2300s. The Next Generation introduces Cochrane as a means of transport used by Starfleet members en route to Enterprise-D. It is used for the same purpose in Star Trek: Deep Space Nine while also playing a chief role in Deep Space 9's Dominion War during which the ship sadly reported numerous casualties.
Uhura
A Reliant-class Federation starship from the 2400s, the USS Uhura was introduced in Picard as a part of the 40-ship armada (that also including a version of USS Archer) sent to confront the Borg Collective's Singularity. Even though the Borgs compromised the Uhura's security after obtaining the security codes of the USS Stargazer, they later reached an understanding with the ships' crew as they had to come up with a united counter-effort to deflect the energy burst from a newly-emerging transwarp corridor. The ship in itself is christened after Star Trek and Strange New Worlds' Nyoto Uhura, communications officer of the Enterprise and later Commanding officer of the USS Leondegrance.
USS Yelchin Was Named After A Star Trek Actor
It is a common naming practice in Star Trek to have ships named after real-life personalities, but with USS Yelchin, the franchise ended up honoring one of their own. The 31st-century starship was introduced in Star Trek: Discovery but was destroyed in the year 3069 due to the galaxy-wide disaster generally known as "The Burn." Interestingly, the destroyed ship's black box was recovered in a mercantile exchange with aliens in 3188. With the USS Yelchin, Star Trek: Discovery offered a touching tribute to Anton Yelchin, the late actor who portrayed Lieutenant Pavel Chekov in J.J. Abrams's trilogy of Star Trek reboot films.