The reason why the people who know her best still call her Eleven or El is simple. The events of Stranger Things season 4 seem to back this up, as some of the branches of the government are trying to blame her for the deaths in Hawkins that are being perpetrated by the terrifying Vecna. After Hopper's apparent death and the extinguishing of her powers by the Mind Flayer at the end of season 3, she relocated to California with Joyce, Jonathan, and Will Byers.
Dr. Owens used his government connections to legally make Eleven Chief Hopper's daughter, complete with a birth certificate, at the end of the second season of Stranger Things. Since escaping from the National Laboratory in the first season of the show, Eleven has found new friends and family. The idea of Eleven being the superhero that the world needs is what the fourth season of the show is leaning towards.
With Vecna being revealed as her original nemesis and a terrifying mirror to her powers, Stranger Things season 4 has already shown that Hawkins will need Eleven the superhero more than it will need Jane Hopper when the season ends. She has loved, lost, and returned to the people she cares about all while trying to discover who she is and what her place is in the world.
Due to her powers, Eleven was taken in by the Police Chief Jim Hopper, who kept her secluded from the world. The hope was for a fresh start and a normal life for all of them, but, as it turned out, Eleven was soon being bullied by other children at her new school. In the fourth season of Stranger Things, Eleven is not using the powers she has had in previous seasons. She left a note for her boyfriend, Mike Wheeler, to say that she has gone to become a superhero again. She is an ordinary girl at the start of the season, and she has a regular name to reflect that. It is clear that Eleven wants her powers back and that she wants to be the hero again. Jane is Eleven's birth name and was given to her by her mother.
Due to her past, Eleven only uses the name Jane in public.
Why is Eleven being referred to as Jane by so many people? She is likely to be a target or an easy person to blame because of her abilities.
It is possible that Jane Hopper is a classic superhero persona for Eleven. The mind was destroyed by the therapy performed on her. There is a warning for the first volume of the fourth season of Stranger Things.
The name change can be considered more metaphorically.