Maybe I'm confused by your wording. He was rounded up by Federals, so the Federal authorities named him a deserter?

I could see the Confederacy naming him a deserter, if they didn't know why he didn't show back up after furlough.

But later, after his name was found on the Prisoner of War register, he ought to have been cleared of deserting.

Unless it had something to do with taking the Oath. But I can't seem to find out what the other options were for Conferate soldiers in Federal prisons.