The holiday is on the official birthday. The sovereign's actual birthday has been separate from the official birthday for centuries, so the holiday does not need to change.
Nah, it's not even her actual birthday. Different countries with the same queen even celebrate it on different days. Presumably it'll be renamed to "king's birthday" but the day kept the same when the monarch changes. Or done away with/re-purposed - there's a general feeling in Australia at least that once the queen dies there will be less support for the monarchy.
... but not for everybody now.