Real World article
(written from a Production point of view)

In the script for Star Trek IV: The Voyage Home, the USS Shepard was a 23rd century Federation starship operated by Starfleet and commanded by Captain Clampett. The Shepard's communications officer was Trillya.

The Shepard was among the vessels disabled by the Whale Probe approaching Earth in 2286.

In the distress call relayed to Starfleet Command from Trillya, it was noted that the ship had lost all power and that the captain had quarantined all but minimal support crew due to failure of bio-sterilization capsules containing the Vegan D virus, which was believed to have infected the entire crew and was responsible for the deaths of fifteen crew members. Trillya further noted that the Shepard's atmospheric regeneration and reclamation systems were nonfunctional, and all medical supplies were spoiling due to the shutdown of refrigeration aboard the ship. She warned that life support systems would be exhausted within eight hours, and requested further advice from Starfleet in resolving their situation.

Information on this ship was from the script. [1]
The Shepard was named after Alan Shepard, the first American in space.