Catherine is SO 20th century (and earlier). To reign in the modern world, you’d need a hip variant of it, like “Caitlyn” or “Katrina” or the like.
Or, indeed, our likely future Queen Consort Kate
Yes. The line of Jacobite Pretender Kings you speak of had previously been united with the throne of Sardinia, and later the throne of Bavaria; but both these unities had split, after son-less marriages, due to different inheritance rules (the Jacobite “throne” passed to a daughter, the other throne to a male dynast).
The “unity” I mentioned of pretender thrones of France, Spain, England and Portugal was based on a difference pretence. Recall that Henry VII claimed England as Heir of Lancaster, but he descended from a bastard son of Lancaster! The legitimate Lancaster heirship was held by Kings of Portugal. (That Portuguese dynasty was eventually usurped by the Hapsburgs but later acquired Spain by marriage!)
These genealogies are silly perhaps, but seem fun!
I sort of like the idea of the Windsors ‘reclaiming’ the very Stuart name of Charles. Yes, its associated with the Jacobites, but who’s going to know or care once Charles becomes king? He even name his second son Henry, and in the event that William dies without heirs, Prince Harry’ll be King Henry IX, firmly displacing the Jacobite Henry IX.
And out of Elizabeth’s brood, Andrew’s name is the unusual one. He was clearly named for Prince Philip’s father, Prince Andreas of Greece, but Andrew is a revolutionary name for a British prince. If QE2 can name a son Andrew, I see no reason why her descendants can’t bring in some new names for their own children, or resurrect some oldies but goodies (yes, including John and Richard).
Well, Zara and Eugenie are unusual names, and Louise is an unusual name for her age.
Andrew does kinda sound out of place, I agree, since you don’t meet many posh people called Andrew in England (some, yes, but it’s more a middle-class and lower name). You do meet a fair few posh Andrews in Scotland, however, for obvious reasons.
Nobody’s going to know or care about whether Charles is a Stuart name, but it’d basically be him naming himself after a King who either got his head chopped off or should have got his head chopped off, and his subjects being labelled Charlatans.
I kinda like the idea that a monarch doesn’t have to use their given name. It’s making a divide between their ‘job’ and their personal self, which is probably an important divide to be able to make when you have little realistic choice about taking on that job.
I’m guessing killing someone, or being jailed for life would rule him out?
Not automatically
Actually Richard named Arthur his heir when he went on crusade, but on his deathbed in 1199 he probably switched it to John. That at least is the story that came out and John was not present at Richard’s death ( but his mother Eleanor was and she would back John over Arthur, probably to the point of inventing such a story if it came to that ). But it would have actually make some sense as, despite everything, Richard seems to have been rather fond of his little brother and Arthur was pro-Capetian, in Philip II’s possession and was underage . At the time of his death, the two brothers had been reconciled and John was serving Richard loyally ( and capably ) as a military lieutenant in Normandy.
England, Normandy and Aquitaine ( still dominated in personality by the aging Eleanor ) sided with John in the aftermath, Arthur’s home province of Brittany and adjoining Greater Anjou backed Arthur ( as son to the elder brother ), which was an insufficient powerbase for Arthur to really claim the throne. So Arthur and John reconciled for the time being. Fighting didn’t seriously break out until a couple of years later during the renewal of the overall conflict with Philip II of France ( Arthur had largely been raised at the French court and was used by Philip as a stalking horse ). Arthur was besieging his grandmother Eleanor at Mirabeau, when John swooped in from behind and seized him and some of his allies. It was only some time after that, while imprisoned, that Arthur “mysteriously” disappeared. Of course as you say it is extremely likely that what everyone suspected is true - John just had him quietly killed and interred somewhere.
Of course the thing with the whole The real King/Queen should be x is that it was pretty conclusivly determined 350 years ago that the legitimate monarch is whoever parliament says it is.
Why do I get the feeling I’m watching the genealogical version of a game of Mornington Crescent?
A game called “And I am Marie of Romania”?
Zara Phillips: Zara Tindall - Wikipedia
There was a passing reference in the 1982 dystopic graphic novel V for Vendetta to “Queen Zara,” indicating that succession had passed pretty far down the line, either due to national disaster or political intervention. Parliament can change the rules on succession at any time, and remove or add whoever it pleases to the line. Personally, I hope the Prince of Wales takes the regnal name “Charles III.” There’s no reason it has to remain forever snakebit.
No British king or queen has ever been numbered higher than VIII, have they? IX and X look a little odd following a first name (unless you’re King Malcolm X).
Of course, now that the thrones of the Commonwealth Realms are theoretically separate (though embodied in the same person), the different Realms could decree that their successions would take place differently. Thus we could have different monarchs in different realms, or even the same monarch known by different regnal names. The same person known as Charles III in the UK and Louis XXVIII in Canada? 
Zog of Albania!
Oh - to have witnessed the Great Richard II Match of 1907. Watley began with a risky Aquitaine opening gambit, but it paid off after Cecilson’s failed attempt at a Plantagenet run. Just reading the match notes will keep you on the edge of your seat for hours.
Henry V
Well, you have to consider that just about everyone was interrelated. Makes the topology of Mornington Crescent look simple!
Alexander II
Of Russia? Of Scotland? Of Macedonia? Or do the rules treat all of them as the same person?
James I of England and VI of Scotland - idiomatically, “Jamie One-and-Six”, so I declare £.s.d.
Is there anything other than James and William where there are separate Scottish and English ordinals already in place (as opposed to Henry IX ans I and the like where an English number exists that’s not duplicated in Scottish regnal history)?
This isn’t the same thing, but there are two lines of Edwards – One from the Anglo-Saxon era and one from post-Conquest.
doesn’t look like it: here’s the complete list of Scottish monarchs.
There’s some interesting names in that list, though - King Constantine, King Lulach, King Eochaid - maybe it’s time for the monarchy to put some of those names back into circulation.