I feel like the nameless isn't actually Cthulhu but based off him. however, if he is that would be rather fun as we could say we survived a dude who destroys minds with a simple glance like 4 times!
(Also, the entire idea of discovering more information via myths and such in Tao's study sounds like it would be interesting, also Tao would prolly get concerned we "happened" to find the SINGLE book about eldritch horrors who have been slumbering for centuries. would be extra funny if he says, "something catch your eye...?" and has the concerned look on his face while we're reading and we can say "hey I've met this dude, who is he?" or just nod or something super casual while he freaks lol. also, making possibilities is fun! people can get better ideas from theories or even just fun ideas that somehow end up being true! plus you get bragging rights if you get it correct.)