The term "Old One" is used to refer to a god or deity, and have been used in fantasy horror and science fiction, quite commonly in H.P. Lovecraft's fiction in various context.
The pictured creature appears to be a member of the species which came to be known as the Elder Things, the term "Old One" being used for several different orders of creature by Lovecraft himself. The Elder Things were introduced in the short story "At the Mountains of Madness," were they are, indeed, referred to by the narrator as "the Old Ones."
Old One resides in the Tower of Wisdom in the Kadath Mandala. Described by Zula as an alien being who shared their knowledge with humans in ancient times. Their language is mostly unknown to even those who live in the Kadath Mandala. Maya guesses that he is hungry and so she gives him a can of crab. The Old One happily takes the can of crab and disappears, leaving the Trapezohedron of Wisdom behind.