Id love to see him reclaim that name now that AE is revived and well. Though, I do think he might prefer the name Phainon the same way Mydeimos prefers to be Mydei, warrior of Okhema, as opposed to the crown prince. Both cause of the familiarity and what he's achieved as Phainon.
More character should call Phainon by his real name.
I think it would do good for him, especially when he buried "Khaslana" with Aedes Elysiae.
Even tho Phainon is his nickname, calling him with his real name would be more intimate to me