From 2361 to 2364, his first officer was Lieutenant Commander William T. Riker. During a mission to Altair III, Riker refused to allow Captain DeSoto to lead the away mission, due to the dangers the planet possessed. Despite this incident, Captain DeSoto had a great respect for Riker and regretted his transfer to the USS Enterprise-D. (TNG: "Encounter at Farpoint") Captain Picard referenced this incident to Admiral Pressman as the reason he selected Riker to be his first officer. (TNG: "The Pegasus")
DeSoto still commanded the Hood in 2366 when his vessel rendezvoused with the Enterprise-D, to deliver Tam Elbrun. DeSoto noted that while the "Galaxy-class boys" aboard the Enterprise-D got to enjoy the frontier, "me, I'm hauling my butt back and forth between starbases." (TNG: "Tin Man")
Background information Edit
In the script for Tin Man, DeSoto's first name is listed as Jonathan in the cast list, but he is called Robert in dialogue. The script also provides some background behind his "put-on" griping, stating it "is an old song going back to when he and Picard served together as lieutenants." 
The Brave and the Bold short story The Third Artifact establishes DeSoto's parents as being Starfleet Captain Mirabelle Brodeur and civilian doctor Hiram DeSoto. It also says that during his time at Starfleet Academy, DeSoto was a member of the "Academy Go team", and team captain in his junior and senior years, winning two out of four Federation championships. By 2371, DeSoto has married, and he and his wife live on the Rigel colonies. The Fourth Artifact indicates that DeSoto remained as captain of the Hood during the Dominion War, and served with distinction during the First Battle of Chin'toka in 2374.
The Star Trek: Typhon Pact novel Paths of Disharmony, states DeSoto distinguished himself in early engagements with the Cardassians, as well as the Jem'Hadar during the Dominion War, and also became quite a diplomat, helping to negotiate treaties with the Cardassians, Romulans, and the Breen. Furthermore, in 2382, DeSoto contacts Picard to inform him of the retirement of Admiral Eric Hasslein from his position at Starfleet Command, and to inform the Captain that Admiral Leonard James Akaar is considering him for the position. He also informed Picard that he is being considered for an Ambassadorship.
DeSoto also appears in the Pocket VOY novel Homecoming, as one of the officers present at the debriefing of Captain Kathryn Janeway, after the USS Voyager returns to Earth from the Delta Quadrant, in 2378. The novel also mentions DeSoto as being on a short list of high-ranking Starfleet officers that may have been involved in the sale of intelligence and technology to the Orion Syndicate.
According to the video game Star Trek: Bridge Commander, DeSoto is the first captain of the USS Sovereign, though he eventually relinquishes this position. The novel Articles of the Federation states he regained command of the Hood by 2380.
In the Pocket TNG novel Losing the Peace, DeSoto is promoted to Admiral and assigned to the position of "Director of Postwar Rebuilding Efforts", following the destruction of the Borg Collective. DeSoto was the second choice for the position, after Jean-Luc Picard turned it down.