I want to number blocks of texts in my work (parts of a movie script or something the creators said) so that I can refer to them throughout the essay. Is there an equivalent to 'Figure' to label these passages?
If they are all pieces of another published work,
See excerpt 6.1 on page 43.
An excerpt in writing is a quoted passage taken from a longer work, such as a book, or poem, or an article. Whatever the subject of your writing or the type of writing you intend to compose, excerpts can be used to 'show' readers what it is you want them to understand and remember about the subject.
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How about sidebar? From M-W:
sidebar: a short news story or graphic accompanying and presenting sidelights of a major story
You could number or otherwise label the sidebars for easy reference.