Answer:
a. So that Mr. Rochester will not be able to find her
Step-by-step explanation:
Jane Eyre doesn't want Mr. Rochester (the man she loves but who deeply disappointed her) to find her, so she gives a false name to Mr. St. John. She says her name is Jane Elliot. That way Mr. Rochester won't know that Jane Eyre is in town.
After a while, St. John finds out who Jane Eyre is, and we learn that the rich uncle of Madeira knew that she had not died and left his fortune to her. It turns out that the rich uncle of Madeira was also St. John's uncle. Such a coincidence that Jane was the cousin of the family who took care of her. Jane, good as she is, decides to share the inheritance with her cousins and has a comfortable and independent life.