By supporting they mean what? Calling the kid the name they want to be called by?

Yes.

(e) “Social transition” means the process of adopting a “gender identity” or “gender marker” that differs from a person’s sex. This process can include psychological or psychiatric counseling or treatment by a school counselor or other provider; modifying a person’s name (e.g., “Jane” to “James”) or pronouns (e.g., “him” to “her”); calling a child “nonbinary”; use of intimate facilities and accommodations such as bathrooms or locker rooms specifically designated for persons of the opposite sex; and participating in school athletic competitions or other extracurricular activities specifically designated for persons of the opposite sex. “Social transition” does not include chemical or surgical mutilation.