Thousands of Confederate soldiers described themselves as deserters to Federal authorities. As far as the U.S. was concerned, deserters were taking themselves off the rolls of the Confederate military, so this was a positive thing to do (in their eyes).
After time passed and veterans wanted to apply for pensions, then the number of deserters dropped off rapidly.
You might check to see if this man ever applied for a U.S. pension. Sometimes they used assumed names when enlisting in Federal military service. My wife had an ancestor named James Witt Abercrombie who deserted his Confederate command. He went to Indiana and enrolled in a Federal cavalry command using the name James Witt. When he applied for a Federal pension as an Alabama resident, he gave both names.