Can I use the name of a passage as class to style, as example, a custom starting screen, like the classic "SEEEEGAAA" screen? Or to check if is the first passage? Or any idea to achieve this?
You need to state which Story Format you are using when you as a question, as answers can be different for each one.
SugarCube assigns an ID to HTML element generated to display the contents of the current passage, this ID is based on the passage's Name and can be used in a CSS selector to style that passage.
That is an 'interesting' way to achieve the result you wanted.
Have you read the Basic Harlowe Passage Tag Based Styling thread, it may give you ideas on other less messy ways to do what you want like using header and footer tagged passages to effect the current passage being shown.
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SugarCube assigns an ID to HTML element generated to display the contents of the current passage, this ID is based on the passage's Name and can be used in a CSS selector to style that passage.
This way I can assign styles before the CSS stylesheet to any element (since I have another rules for body out of the "sign" screen.
Have you read the Basic Harlowe Passage Tag Based Styling thread, it may give you ideas on other less messy ways to do what you want like using header and footer tagged passages to effect the current passage being shown.