Why did Chris revert back to his original name on the S.O.S note?

I think Chris had an epiphany during his last days in the Alaskan wilds. Chris discovered that he needed other people and that the person he used to be was very much still part of his identity. Alexander Supertramp was merely a moniker that Chris could hide himself behind. Chris was his real name and the letter was addressed to those who loved Chris and missed him.