This is an interesting situation.
Regarding the choice of parent categories, there's a straightforward solution: Both Gary and Merrillville should be parent categories for this school.
The school category name is a bigger challenge. A high school category name should include a location, but this school has two locations. And if we choose one of the possible names, we can't use redirects to send people to the correct category. Wikitree can redirect a profile name to a new name for that profile, but doesn't have a mechanism to redirect a category to a new/different category name. (The difference between profiles and categories also helps explain why you can't link your question to a category.)
I think the best solution would be to:
- Name the school category either Andrean High School, Indiana or Andrean High School, Merillville, Indiana (with preference for the latter name)
- Put the school category in the parent categories for Gary, Merrillville, and Lake County Schools.
- Put notes on the category pages for all three parent categories to explain that the school was in Gary from 1959 to 1971, but has been in Merrillville ever since that city was incorporated in 1971.
Hopefully, anyone searching for Andrean High School or wanting to add its category to a profile will recognize the category Andrean High School, Indiana or Andrean High School, Merillville, Indiana as the correct one. And since it was only part of Gary for 12 years, there's no particular reason to choose to leave that city's name in the category name. Categorizing it by its modern location would be consistent with the way that university categories are named by the institutions' current names, not their historic names.