So then what's Link's last name
You know, this is actually a really interesting question. Of course, there is no official answer, and it is likely to vary wildly due to how Link is a different person in each Zelda game. However, there is plenty of room to speculate!
Now, a very likely answer is that Link doesn't have a surname at all. The use of family names is not at all consistent across human history. In European countries, it is a fairly recent development that got its start in the 11th century and only slowly spread from the aristocracy down to the common people. However, the Zelda series is usually set in a Hyrule that is very loosely based on Late Medieval or Early Modern Europe, times where the use of surnames were catching on with common people.
In the case of OoT, there is absolutely no way that Link has a family name, since he is an orphan raised well away from human civilization. It is far more likely that if he grows up and gets married, he would simply take the family name his wife uses. Alternatively, he could take something related to the Deku forest or the Kokiri as a last name if he was knighted or such. If the Link from Twilight Princess is descended from OoT Link, then he might still be using such a family name. Of course, it is still possible that TP Link could not have a family name at all, being a commoner living in a region so remote most people in Hyrule aren't familiar with it.
On the opposite side of the spectrum, the Link from ALttP almost certainly has a family name, being a descendant of the Hylian Knights whose uncle is an active knight. The same is true of the Link from Breath of the Wild: his father was also a famous knight. In both cases, they may even be related to branch families of the Royal Family of Hyrule. It is pretty much impossible to guess what those family names would be, though.
Minish Cap offers the most interesting material to extrapolate a last name for Link though. In Minish Cap, Link is raised by his grandfather, a blacksmith that everyone just refers to as Smith. Now, Link regularly went to school in Hyrule Castle Town as a child in the backstory for Minish Cap. The chances that there was another kid or other person named Link in a large city was pretty good (since it is apparently a pretty common name, considering there are multiple Zelda games where you meet another person named Link). So, it is very likely that Minish Cap Link has a surname, or at least a byname. Now, if he just has a byname, it would be definitely be "Smith's grandson", considering how famous Smith is. Furthermore, such bynames evolved into a very large percentage of European surnames, for example Miller and Baker are fairly common English surnames. So, Link's full name in Minish Cap could very well be Link Smith or Link Smithson or some other variant. If Link takes up the same occupation as his grandfather when he grows up (a likely possibility, considering Link was an apprentice blacksmith in ALBW), then the odds of that being his last name increases.
On the other hand, Zelda has very low odds of actually having a last name. She is the daughter of the Hyrule Royal Family, so Princess of Hyrule does a perfectly good job of describing who she is. In the real world, neither the Emperor of Japan nor the Queen of England use last names. The current Emperor of Japan is just named Akihito. When addressed by people, they just call him the equivalent of Your Majesty the Emperor. When he dies, his name will be changed to Heisei Tennō (essentially, Emperor of the Heisei era). Elizabeth II's full name is Elizabeth Alexandra Mary. Despite being part of the House of Windsor, Windsor isn't used as her last name. Again, Queen of England is a sufficient description that using a last name isn't necessary. It's usage is very uncommon.
So, it is vey likely that Zelda is just Zelda. Different Zeldas may have the equivalents to middle names to differentiate them, but those wouldn't be real family names. On the other hand, it is very likely that a Princess Zelda who ascends to the throne of Hyrule would take a different name as a reign name. The Hyrule at the end of the name of the kings of Hyrule might be limited in use to the current reigning monarch, since we never see it used anywhere else.