BE-spelling company name in a US file (or vice versa)

If you're working on a US file and a company/product mentioned spells their name using British English, use their spelling when referring to their company or product, but use US spelling in the rest of the text.

US file: Walnut Street Theatre is one of the oldest theaters in the US.

The same rule applies for British English files that mention something with US spelling in the name: spell the name as they do, but use British spelling in the rest of the text.

British file: Many global organisations, such as the World Health Organization, gathered to discuss the issues.