Tyson uses names in a variety of ways.
When he’s nervous, Tyson tends to overuse names to the point of hampering his words to the point of being difficult to understand.
More generally, Tyson uses people’s names to put them at ease, then as a way of calming himself; with the knowledge that the implied familiarity of using someone’s name will help reduce his social stutter. And then, simply out of habit, even when he no longer stutters around a person.
As well as using names to create an artificial closeness, Tyson’s choice of name can be used to create distance and separate out different parts of his life. He adores Darling with all of his heart and is glad to be his loyal Pup, his hands are soaked in blood for Moriarty, and Jim is the beloved - if exasperating - Irishman that Tyson must bribe to take sustenance.
Sebastian is the man Tyson, foolishly, loves and would gladly die for. Moran is the sniper who’s talents he respects and the commanding officer snapping at him like a hound lashing out. The Colonel is the one who beat Tyson bloody then abandoned him for dead.
Anthony Hawthorne is Tyson’s default cover name, borrowing the name from his Great Grandfather, and Sebastian publishes his books under the false name, Zachary M. Cohen. If given time to develop into its own personality, The Soldier would take the name Anthony eventually.