"Rufus" is an example, Gracie, of an "unusual" name. But it has royal precedent. In reading history of earlier years in the UK, going back centuries, I have found other Rufuses than the child of Lady Rose Gilman. The name Aiden may be unusual, but it is the name of a medieval saint of the UK who was very famous in his day, and you will find a few little boys with that name, probably with parents who knew their history. Jayden does not sound like it has any UK significance, but I could be ignorant on that score.
In other words, "Aiden" is not an odd ball name. "Rufus" may be slightly odd ball. I read that it is used for redheads. I wonder if Rufus Gilman is a redhead? Probably.
Lady Rose probably wanted a name with tradition which was unusual. In other words there is a big space between "Aiden", a UK name with great tradition, and "Rufus", which has an obscure tradition. I think. I am not the ultimate expert on history. Someone like Ish probably knows more.
St. George supposedly was a saint of the UK too, but I wonder if he is more from mythical lore than Aiden. Aiden we know was a real human being about whom much was written in his own day. No one seems sure if King Arthur was a myth or a real human. He probably was human but his story has probably been turned inside out and rightside up by centuries of retelling. One thing is pretty sure from history about Arthur; he died violently as did most of the leaders of his day. To be an early Celtic king was to be destined to die by the sword.
The royal connection to "Rufus" is King William II, known as William Rufus. He was the son of William the Conqueror and was killed whilst out hunting in the New Forest. He reigned from 1087-1100. Succeeded by his brother Henry I.
"Rufus" was because of his red-faced appearance; he was v unpopular. So it is a description of the king, not a name.
St George is the patron saint of England.
Rufus is a Latin name meaning "red-haired." In addition to William Rufus, who either got the nickname due to a red face or red hair (I've seen both claimed, and am inclined to believe it's the hair because of the name meaning), it's also the name of Saints and is even mentioned in the bible.
I doubt Rose Gilman picked the name because of William II. To me it seems more likely that it's a name her and her husband liked.
Aiden is an Irish name, and reportedly rather popular throughout Great Britain. According to behindthename.com it's the 61st most popular name in England and Wales, and the 36th most popular name in Scotland.
Saint George is a real person; scholars have said that there is no doubt that he existed, although little faith can be put into the stories about him. (Atheist scholars say similar about the existence of Jesus).
The story of George is that he slew the dragon - the dragon here is a stand in for the then pagan Roman Emperor, to which George stood up to. At a time when Christians in the army were being persecuted, George (who was a soldier and a Tribune) stood up to the Emperor, denounced him, and declared himself a Christian. He refused to renounce his faith, and was executed for it. George was an obscure saint in England for a long time, only really gaining recognition in the 14th century - likely because of the fact that he wasn't associated with England and this wasn't closely associated with anything specific. When the Reformation happened and saints were effectively tossed out the window, George was the only one kept (ironic, given as the man previously held as a patron saint had been Edward the Confessor).
The general consensus on King Arthur is that he wasn't likely a real person - and if he was, it's likely that he was actually a composition of several people. While he's believed to have lived in 4th-6th century Britain, no source mentioning him predates the 10th or 11th century. No one individual can be seen as the source for the myth. There is the idea that he may not have been a king at all, but rather simply a soldier or a leader in battle. There's also the idea that he may have been a folklore hero or forgotten deity to whom actual deeds were attributed to.