Jeremy Bentham on Lost is not a separate character. It is an alias used by John Locke after he leaves the Island.
Basic identity
On the mainland, Charles Widmore provides Locke with the false name “Jeremy Bentham” so he can secretly contact the Oceanic Six and persuade them to return to the Island. In flash‑forwards, the dead man in the coffin known to Jack and Kate as Jeremy Bentham is eventually revealed to be John Locke.
Role in the story
Using the Bentham identity, Locke travels the world visiting the Oceanic Six, trying to convince each of them that they must go back, but he largely fails. After this failure, he is murdered by Ben Linus, and his staged “suicide” as Jeremy Bentham becomes the catalyst that pushes the survivors to return to the Island.
Later significance
Locke’s body, still known to the outside world under the Bentham identity, is taken back to the Island on Ajira Flight 316 as part of recreating the original crash conditions. Once there, his corpse is used as the physical form for the Man in Black, who impersonates Locke to manipulate the remaining survivors.