Example, the supreme court of Manitoba is now called “The Court of King’s Bench” – but the URL still says queen: https://www.manitobacourts.mb.ca/court-of-queens-bench/
Double takes abound. There should be a non-gendered form to use. “Court of Monarch’s Bench” or something ;)
The Royal Navy figured this out a long time ago. Just call it HM’s Ship. Works for both Her Majesty and His Majesty. Don’t ever need to repaint the name on the side of the ship.