What is the significance of Jane choosing Elliott as her last name alias in Jane Eyre?
This is a difficult question, but it is most likely an homage to Mary Ann Evans, known more commonly by her psuedonym, George Eliot. Eliot was a contemporary of Bronte, and the two authors (along with Emily Bronte) stand as the greatest female authors of the Victorian Age.
All three women used male psuedonyms to validate their writings, because the novels would most likely have been dismissed out of hand as the work of women. Eliot's most famous novels are Middlemarch and Silas Marner.