Although the kings of Hoshido and Nohr were/are King Sumeragi and King Garon, respectively, those are also the family names passed onto their respective children. The full names are as follows:
Ryoma Sumeragi (皇 龍馬 ; kanji means “dragon horse”)
Hinoka Sumeragi (皇 ひのか ; unknown kanji equivalent)
Takumi Sumeragi (皇 拓未 ; kanji meaning “clear future”)
Sakura Sumeragi (皇桜 ; sometimes written as さくら)
Xander Garon
Camilla Garon
Leo Garon
Elise Garon
Also, I have this idea that “Garon” is pronounced “Gah-ROHn” with a nasal inflection and the final “n” slightly silent, much like a French accent.
I've been reading some Fates headcanons, and it makes me want to jot down some of my own headcanons. I'll start with my hc of the Royal children's ages:
Because I'm a huge nerd, I based them on evidence through the games and supports. Let's start with ages when Corrin got kidnapped (hereforth known as "The Kidnapping")
Through the story and supports, Corrin does remember a little bit about growing up in Hoshido, albeit not very much. This means that they had to have been at least 3-4 years old during The Kidnapping, because of childhood amnesia (ie the theory that babies either don't form episodic memory until 3-4, or they forget about the memories formed before then later in life). So my hc is that Corrin was 4-5 during The Kidnapping, since I think they had a couple years of memories from Hoshido.
Ryoma said in Corrin x Ryoma S support that Sumeragi trusted him with the secret that Corrin isn't Sumeragi's child. This makes me think that Ryoma would have been old enough to be trusted with this secret before Sumeragi died. So I think Ryoma is 13 during The Kidnapping.
Hinoka was young enough that she cried a lot right after The Kidnapping, and lashed out at Mikoto after she became the new queen (her support with Corrin), but also old enough to realize/understand what happened to mourn the loss of Corrin (and have the desire to get them back). So I place her at 7-8 during The Kidnapping.
Sakura said in her support with Corrin she heard a rumor that she was the one who was supposed to get kidnapped. Regardless of the truth of the rumor, it means Sakura was at least born during The Kidnapping. I think she'd just been born though, since I don't think she's that much older than Elise (more on Elise in a sec), so I place her at 0-1 during The Kidnapping.
Takumi is at least 9 months older than Sakura, but is younger than Corrin, so he could be anywhere between 2 and 4. But I put his age at 2-3 during The Kidnapping by working backwards from present day age. Plus he doesn’t remember Corrin at all when they met up in present day.
Elise had not been born yet during The Kidnapping, because in her support with Azura, Azura said she heard about Elise being born after Azura had been kidnapped to Hoshido. So Elise is about 4-5 years younger than Corrin.
Those are all the evidence provided by The Kidnapping. Now let's look at present day.
Elise is the youngest of the siblings, yet she's able to have a child, which means she's past puberty. I place her at 14 at the youngest. Which means that Sakura is 15.
This means that Corrin is 18-19 present day, which I think fits; they're old enough to make important decisions but young enough to be sometimes not rational, and for their older sibs to treat them like a kid sometimes.
Leo is younger than Corrin, but he acts more mature than Takumi, so I think he's older than Takumi. Yet he still does irresponsible things (eg Nohr drama CD) so I place Leo at 17, and Takumi 16-17.
Going off Corrin's age and the age differences calculated from The Kidnapping, it means Ryoma is 27-28, and Hinoka is 21-22.
With Xander and Camilla, I don't really see that much evidence to place their ages, other than Camilla seems younger than Ryoma but older than Hinoka (acting all motherly). So my hc is that Xander is slightly older than Ryoma 'cause he acts all dad-like, and he just _looks_ older (maybe it's the forever wrinkly brows). So I place Xander at 28-29, and Camilla at 26-27.
Now we have Azura (don't worry I didn't forget about her). Most people think that she's around the same age as Corrin, but I disagree; I think she is at least a few years older than Corrin. This is because in Revelations, she remembers stuff about her mom, and the things her mom taught her about Valla. This makes me think that she's 5-6 when her mom died. Plus, she has more vivid memories about her time in Nohr than Corrin does about Hoshido, which makes me think she was older than Corrin was when she was kidnapped.
The timeline goes like this: Azura’s mom dies => Garon going crazy and evil => The Kidnapping => The Revenge Kidnapping. I don't think there's a huge time gap between The Kidnapping and The Revenge Kidnapping, maybe a few months. But I think there's some gap between Garon going evil and The Kidnapping (he needs time to plot and stuff, plus there was the period of time that Azura suffered in Nohr after her mom died). So I think Azura is ~7 during The Kidnapping. This would place her at 21 present day (ie she's only a few months to a year younger than Hinoka).
In conclusion, tl;dr, my hc of their ages:
Corrin 18-19
Azura 21
Ryoma 27-28
Hinoka 21-22
Takumi 16-17
Sakura 15
Xander 28-29
Camilla 26-27
Leo 17 (older than Takumi)
Elise 14