In the multiple editions of the The Legend of Zelda franchise, have we ever learned Princess Zelda's full name?
Does she simply just go by the name Zelda or perhaps Zelda of Hyrule (a more classical last name derived from the country)?
Assuming she follows the same patterning as her relative (King Daphnes Nohansen Hyrule) her full name and title would be Princess Zelda Hyrule.
That being said, her name is given in all of the games and additional materials as simply Princess Zelda, so it's far more likely that her name is a mononym and that her full name (including formal title) is "Princess Zelda of Hyrule", as noted in the instruction manual for The Legend of Zelda - Four Swords Adventures.
I have come to the conclusion that Nintendo sucks at naming characters... After much looking it seems that she is simple Princess Zelda or Princess of Hyrule, Princess of Destiny, Her Majesty, Spirit Maiden.
Other than the few times she has appeared in games as other characters (I dunno why). She has appeared as Sheik, Tetra, The Leader of the Sages, The Goddess Hylia.
I have managed to dig up the fact that she was named after F. Scott Fitzgerald's wife Zelda Fitzgerald.
Shigeru Miyamoto stated that the Princess Zelda's name originated from Zelda Fitzgerald, the wife of the acclaimed author, F. Scott Fitzgerald. The name "Zelda" ultimately derives from "Griselda," which may come from the Germanic elements gris ("gray") and hild ("battle").
I think someone needs to talk to Nintendo about properly naming there characters! Or at least making an official list of their names like "Yes this character is called X".
There is no canon answer to this. Only a handful of Zelda's relatives are mentioned throughout the games. Many of them go unnamed but there are a few that are named, all of them kings. King Daltus from The Minish Cap has not last name, and neither does King Harkinian from the comics, cartoon and games of dubious canoninity.
The interesting one is King Daphnes Nohansen Hyrule from The Wind Waker. His last name is the same as the realm's name, which befits a ruling monarch. He did have a daugher, the antediluvian princess of whom we see a painting in Hyrule Castle. If her name was Zelda then in that case she was Princess Zelda of Hyrule.
So what is this "Hyrule", then? When one has a noble title this is often referred to as "of X". This does not mean that this is your last name: it's a title. Real life princesses like Princess Amalia of Orange-Nassov can have this (this particular princess has three of such titles), but only one refers to her dynasty (but no family name). As for the actual name of Hyrule in Daphnes Nohansen's nme this is an interesting case: it seems to be his actual last name. Where does this come from? I am uncertain, but if I had to use conjecture I'd say that he's the product from another family whose name is actually Hyrule.
So what does this mean for Zelda's name? Well, her name's just that. Zelda. The afmore-mentioned king would be Daphnes Nohansen Hyrule. Including their titles this would be Princess Zelda of Hyrule and King Daphnes Nohansen Hyrule.
: The Minish Cap was developed by Capcom, not Nintendo. It is unknown if these two issues are related.