The question of name may not have come up. It's common for hikers along the Appalachian Trail to "rest" a few days at farms in return for a little work. The farmer may not have realised that the guy didn't know his own name and instead have thought it none of his business if the guy didn't want talk about personal stuff.

And it might not have seemed that unusual to the lost guy either. He's of an age where he might have done that sort of thing as a matter of course while travelling if he grew up rural. Hotels were for rich people and my dad traded work for a few days sleeping in the barn in bad weather in the 1940s. There's a glimpse of bygone rural life in the stories of the farmer's daughter and the travelling salesman in the barn....

I think the problem is that he had a workable plan - go to Asheville - and he was able to carry it out. Had he had been totally helpless he'd had been noticed or found earlier.