It has no name, simply being the Jellyfish. It speaks telepathically through electrical-pulses that directly affect the human brain. Not much is known, but it definitely probes deeper into memories than necessary.
Quill loathes the Jellyfish. She blames it for her near mental collapse into insanity. Despite this, she couldnât kill it -- it was her only company. Now that she has R-41N and Penny, things have changed. The Jellyfish knows she is planning to kill it, so it hides from her.
Like Penny, R-41N physically canât communicate with the Jellyfish. There is even more of a communication barrier because it cannot write. He does know about the strain it has caused on Quill. This combined with the fact that it (allegedly) calls him Dillian is enough to earn R-41Nâs discomfort.
Penny has never spoken to the Jellyfish, and does not plan to. She hears Quill muttering to herself about it every now and then, so she keeps her distance. The Jellyfish knows that it and Penny are kin, but Penny is oblivious.