But apart from hiding your physical appearance, isn't the divine connection established through for example initiation something that would be somehow exposed when interacting with the same or another cult?
Could you be a Wind Lord of Orlanth from the temple in Boldhome, but pretend not to be so when you get to Nochet, and initiate ("secretely again") into the cult of Orlanth there?
I would guess the divine connection established through the sacrifice of POW and MPs would mean something more than physical appearance.
Can you fake initiation? "Sure, I sacrificed POW and now have access to Orlanth's special rune spells. I just don't want to use them."