Not much is known other than he is the husband of Beryl and that he lives in Armadillo.
Red Dead Redemption
Marston finds the concerned husband outside of the Sheriff's Office in Armadillo as part of the American Appetites stranger mission. He is very upset that her wife, Beryl went missing. He tells Marston that she was last picking mushrooms in the hills near The Hanging Rock.
Jeremy's name is not revealed anywhere in game, but his name is revealed in the file containing his dialogue, which is "jeremy_parsons01.awc".