The mind flayer (illithid) is a humanoid with an octopus-like, tentacled head, a predator that devours victims’ brains and dominates their minds. The idea of an octopus-headed monster clearly bears the influence of Lovecraft’s Cthulhu iconography, but the name "mind flayer / illithid" and this specific design are Product Identity of Wizards of the Coast, excluded from the OGL/SRD and protected.
So the concept (a tentacled head, mind-eating) is treated as a shared motif of the cosmic-horror lineage while the name and particular form are made clear as trademark. Its premise — an alien race that crosses the planes and enslaves minds — overlaps exactly with cosmic horror’s motif of intrusion, the thing that seeps in from outside and eats away at the human mind, joining dungeon fantasy to the Lovecraftian tradition.