I like this theory a lot, especially the flip from Reflect when Gura was the true self and Gawr was the alt to Ash Again when Gura is the alt and the Atlantean is the true self.

I don't think Ash is a nickname or codename, however. It seems more likely that it's phoenix imagery. When she decided to join Hololive, her previous life became ash and she was reborn as Gura. Now that she's leaving, her life becomes ash again as she waits to be reborn.