Q. Do we refer to fictional characters by their first or last name?
A. Either, neither, or both. In fiction, people are known by the names they’re called, typically by the narrator but sometimes by others (as in dialogue). In other words, whether you’re referring to Huck Finn or Jo March or Edward Casaubon or Heathcliff or Juliet or Romeo or Elinor Dashwood or Don Quixote or Miss Marple (or Miss Jane Marple if you prefer, at least on first mention), you can usually take your cue from the novel or story or play or other such work that features them.
You can do the same for any mentions after the first, as in Huck or Jo or Casaubon or Heathcliff or Juliet or Romeo or Elinor (not to be confused with Mrs. Dashwood) or Don Quixote or Miss Marple. When more than one form could be used, shorter may be preferred over longer, as with Jo (who is rarely “Josephine” in Little Women) and Huck (as he’s usually called in Huckleberry Finn even when the last name is used, in spite of the title) and Casaubon (even though, in Middlemarch, he’s called “Mr. Casaubon” five times as often as “Casaubon”).
Speaking of George Eliot’s quixotic, tragicomic scholar (Casaubon, that is), you could likewise shorten “Don Quixote” to “Quixote,” even though that more famous character is rarely mentioned without his honorific in the four-hundred-year-old novel that brought him to life.
Though all the characters mentioned above are from older classics, the principle for newer works is the same—as it is when you’re writing the characters yourself—though there will always be some exceptions.