The Cologne cathedral took over 600 years to finish because the original plans got lost along the way. it was paused after 300 years! For the following centuries, many generations only saw the same unfinished state with the crane on top.
Most cathedrals and monuments are like that because until recently in human history, they took a long time to build and so the original architect would die, the financing might collapse, etc. Heck, this happened to Gaudi; the remarkable thing here is that the people after Gaudi wanted to continue his vision as much as they could.
The Washington Monument in DC, for example, famously is different colors because they had to change the source of marble during construction when funding halted for a time.
Fiction, but you if wonder about things like this, you might be interested in The Pillars Of The Earth series about the building of a cathedral in 12th century England.
Not sure “celebrities” were such a thing as they are today. 7 centuries was before the reformation and things were pretty austere. Surely nobles celebrated things and there were favored artisans but celebrated as crassly as we do today in such abundance. I don’t think the media existed to allow that to take place.
Eh, they certainly weren't celebrities in the same way, that would only be possible with modern broadcast media. But people like the pope, kings, and dukes would be pretty close. I would expect the average medieval peasant would know who the pope (or popes, depending on the date) were, and at the least who their king was, as well as the relevant nobles for their village. And I wouldn't be surprised if they knew who the neighboring kings and nobles were. A peasant from the Iberian peninsula might not know who the king of Poland was, but they would likely know who the French king was and likely who was emperor of the Holy Roman Empire.
And medieval people definitely built monuments to themselves. A great example is Battle Abbey [0]. The official reason it was built was as penance for William the conqueror killing so many English, but there is definitely a strong case to be made that building such a grand abbey was in 0art to signify the new Norman rule and to remind people of who was in charge. They weren't venerating the architect, but it was very clear to everyone who paid for the abbey and William remained very much linked to the structure. That would have been one of the most impressive buildings for a very large area, even it's ruins remain impressive nearly a millennium later. It's a religious building, but it was even at the time very much linked to a secular ruler (inasmuch as the rulers of the time were secular).
It really depends on what you mean with "know" here.
The legend say that when the king tried to flee the revolution he was only recognized due to a coin with its face engraved in it. A teacher taught me this one with a variant where the king itself gave the coin to pay in a tavern. Now even it is just a legend, that also gives an interesting reflection on what it means to be famous at this time.
A typical Iberian peasant probably wouldn't have heard of Poland. The King or Emperor would be "the King" or "the Emperor" and might as well live on the Moon.
Not many people realise that the more distant locations in Shakespeare's plays were close to science fiction. If you were a British peasant visiting "Verona" or "Venice" was like visiting the ISS. You might get swept up to fight in France, and there was a tiny chance of joining the navy. But most people spent most of their lives within a tiny area, with little idea of what was happening elsewhere.
So cathedrals were stunning. If you somehow visited a cathedral city you'd be struck dumb by the size - unimaginable to someone who grew up on a small holding.
