They have the same rank, name, lived around the same time, and Wikipedia doesn't have a page on Abner Small. I need it for a project but I can't get any farther without knowing.
Abner R. Small was a company and then field grade officer (Major) in a pretty well known Maine regiment. Like most low ranking Civil War officers, he was a volunteer rather than a professional. https://www.mainememory.net/artifact/4305 He also wrote some memoirs that are fairly well known.
Doubleday was a Major General (a different, much higher rank) and a professional military man who attended West Point. It would be a bit odd for him to use a pseudonym and I don't think there is any evidence that he did so.