Increasingly, it looks like the question Harry and Meghan must be asking is if there’s anyway to take the passports away from her family. 
It’s “Her Britannic Majesty” in diplomatic parlance, to distinguish her from other monarchs, as SanVito’s link in post 30 shows.
HM.
And things worked out just fine for him.
Band name!
I wasn’t using diplomatic parlance.
Unless The Whistle Blows.
Well, it’s never “Her Most British Majesty,” unless you meant it as a joke.
I find this hard to believe, but I have no idea what Prince Harry’s name is–on his passport or his underwear in the laundry.
Is it Harry Wales? (ref also in the current Windsor Threadapalooza.)
His passport probably doesn’t say Harry Wales. British passports include the titles of the passport holder.
His full name is Henry Charles Albert David. Before his marriage he was Prince Henry of Wales (since his father is Prince of Wales), commonly known as “Prince Harry.” Since his wedding day, he is now Duke of Sussex, Earl of Dumbarton and Baron Kilkeel (a trio of English, Scottish and Northern Irish titles, respectively). He was referred to as “Officer Cadet Wales” at Sandhurst, the British military academy.
For more: Prince Harry, Duke of Sussex - Wikipedia
According to that paragon of truthiness The Daily Fail, Meghan has expressed a desire to one day become President of the United States.
This would rule out a citizenship change. End of discussion. 
Poor bastard has no last name.
But it wouldn’t rule out her becoming a British Citizen while remaning a US Citizen, would it?
His last name is David. That’s the last one. 
“Prince of the Royal Blood” looks pretty cool on a passport.
No, it wouldn’t. But for political reasons Ted Cruz renounced his Canadian citizenship when he ran for president. There was no legal reason requiring him to, but he chose to in order to avoid questions of divided loyalty.