Use of an alias was actually not uncommon. It seems to be found more often in the Navy than the Army for some reason.
The reasons are many. Basically, there is some reason that the person did not want their real identity readily available to recruiters and those officials who would look over the rolls. They may have been underage, and did not want the recruiter to try to locate a relative to sign for them (because, perhaps, they would not). They may have simply wanted to enlist without their family finding out immediately, and thought that this would help (don't forget rosters of new units often appeared in the local newspaper). Some men were ducking bill collectors. Some were in trouble for something and wanted to "disappear." Some may have simply been trying to escape from bad family conditions.
The alias was easy to use in this era before people carried forms of ID. However, in later years, when the men tried to apply for pensions, it created havoc, and some men due pensions were unable to collect.