The USS Equicon was a Federation starship that was in service with Starfleet in the mid-24th century.
In 2364, Lora Trimble was Captain of the ship.
That same year, Captain Trimble received orders from Admiral Kathryn Trimble of the Starfleet Operational Support Services pertaining to the transfer of personnel. Starfleet officers to be transferred included Lieutenants Carol Mathews, John Testa and Jon Stevens, Commanders Bjo Trimble and John Trimble and Doctor Jennifer Jumper.
At the end of that year, Data read these orders and several others to investigate claims of a conspiracy among the highest members of Starfleet Command. (TNG: "Conspiracy")
This ship was presumably named after the series of Equicon conventions, originally organized by Bjo Trimble. One such convention took place in the year 1988, hence the ship's registry.