I've never thought that demon like shape on his tunic made much sense. Isn't he one of the good guys? A heavily stylized tree of life symbol would have been more appropriate. Perhaps five arms/branches, two each side, all terminating with a circular device of some kind, with the top one ending at the the Eye of Agamotto. There's a tradition of something similar to this with some tribal shamans having a tree of life on their robe/tunic relating to their travels within a spirit world Tree of Life. Through the inside of trunk and branches to other worlds at their terminals.

I guess Ditko wanted Strange to appear spooky and dangerous in the first story, and the demon shape sort of stuck.