The ship's registry appeared in the okudagram depicting the tachyon detection network in "Redemption II". According to the Star Trek Encyclopedia, the class of this starship was Renaissance級. In the first edition of the Encyclopedia, and later corrected, the Hornet was given the registry NCC-10523.
According to the Encyclopedia, the ship was named after the American aircraft carrier USS Hornet (CV-8), which saw action at the Battle of Midway, but was later sunk in October 1942. The named then passed to CV-12, launched in late 1943. Hornet CV-12 also had a link with space exploration, serving as the recovery vessel for the Apollo 11 and Apollo 12 missions.
Ironically in "Redemption II", Starfleet's Hornet served alongside USS Akagi, a ship named after a Japanese carrier that fought against the real life Hornet at Midway - episode Ronald D. Moore thought it fitting that, in a future where Humanity had become united by its own accord, ships whose namesakes had fought one another would now fight side-by-side.
According to the Star Fleet Technical Manual, there was a Constitution級 USS Hornet in service in the 23rd century with the registry NCC-1714 (although the game supplement Federation Ship Recognition Manual gives its as registry NCC-1778). This would seem to be the same Hornet that was mentioned as a combatant in the novel Dreadnought!. According to the DC comic book "Gateway", she was captained by the sister of Edward Hagler.