Wasn’t Prince Philip of Greece in the navy before renouncing his title and getting British citizenship? And the British royal family had German titles until 1917 when they renounced them due to anti German sympathy in WW1. Hence Princess Victoria of Battenberg becoming Marchioness of Milford Haven.
A big question is what is the purpose of the monarchy? Is it merely symbolic? Does it operate under the foreign service? I think the degree of transparency ought to reflect its function. At the end of the day, they are public employees who work for the people of the UK (of which I am not included). As an outsider, I would think that the British people would want full transparency and the ability to strip royal members of titles when they are no longer found to be appropriate representatives of the nation. In other words, the people should be able to force Charles to strip Harry of any royal title and let him live a je ne sais quois life as his son, Mr. Harry Mountbatten Windsor.
Philip wasn’t exactly an outsider, though - he had direct descent from Queen Victoria through the maternal line. Queen Victoria >Princess Alice>Princess Victoria >Princess Alice >Philip. All the repetitions in names makes it quite confusing !
I’m not sure what you mean about the monarch operating under the foreign service ? The reverse would be true - the Foreign Office is part of the Government which is actually officially His Majesty’s Government. ( Still seems weird to say His rather than Her Majesty
) Our tax collection system is HMRC ( His Majesty’s Revenue Collector ) Our coinage and notes ( the Royal Mint ) and our stamps ( the Royal Mail ) have the Monarch’s image on. It’s the Royal Navy, and the Royal Airforce - the Monarch is head of all the military. They are the head of the Church of England, which, though we are by and large an irreligious country now, still has an official role - the bishops sit in the House of Lords. Even a prison sentence is ‘being detained at His/Her Majesty’s Pleasure ‘ in a prison eg in HMP ( His Majesty’s Prison) Wormwood Scrubs. There’s many more examples.
They aren’t ‘public employees who work for the people of the UK’ in that sense - a British citizen is a subject of the Monarch, and those who gain citizenship other than by birth, have to swear an oath of allegiance to the monarch as part of the process. A British passport is issued in the name of the King or Queen.
It’s deeply woven into into our public life - the concept of the monarchy needs to be separated out from the members of family in place at any one time, though this twerp is doing his very best to bring both down.