Asklemmy

The village "Wacken" is well known in Germany because they hold one of the worlds largest anual Heavy-Metal festivals. They have a population of around 2000, the festival regularly attracts around 80,000 people.

Probably Dildo, Newfoundland.

You know why.

Edit: Actually, I think Dawson City is smaller. It's famous for being a big city back during the gold rush, despite being up near the arctic circle.

Wąchock in Poland, (in)famous for being the place where tons of jokes happen, population around 2800.

Also Jeruzal, though known under its fictional name of Wilkowyje, the place where famous TV show "Ranczo" was made, population around 340.

Not a city as much as part of a city, but Coney Island is pretty well known. I was recently speaking to someone in Colombia and even they knew of it!

(I'm part of the sideshow cast ☺️)

In Denmark it's probably Snave (No English Wikipedia page for it). Population is a whopping 211 people. It was popularized in a series of commercials for a Danish cellular carrier. The concept was so popular that there even was a movie. I haven't seen it, but the reviews seems to suggest it could be fun to watch... If you are drunk enough.

The word "snave" in Danish can somewhat be translated to snogging in English. Heavy kissing. Which has led to the city having massive problems with theft of their signs.

Hallstatt - Austria

The city so beautiful that the Chinese copied it.

Regina, the city that rhymes with fun!

Edit: I just realised the question was recognising the name of the city, not recognising city based on a picture...

Probably Svolvær/Lofoten with a population of ~4700. It doesn't have the official status of "City" in Norway though.

I don't know about the smallest, but I've always thought that Santa Fe, New Mexico has an outsized influence on everything from food to art to architecture and culture. I visited last year and it was much smaller than I envisioned, partly because there are local regulations on building height to keep from ruining the charm of the city.

How about: name a country and name the smallest city you recognize from there. Like New Zealand you could say Rotarua

Lajitas, Texas, which once elected as their mayor a goat that drank beer, has a population of 75.

Terlingua, Texas, as made famous by Jerry Jeff Walker and home of the Terlingua International Chili Cook-off, has a population of 78.

Luckenbach, Texas, as made famous by Waylon Jennings and Willie Nelson, has a population of 3.

What do you consider small? A lot of people know Cupertino California because Apple are based there, but it's only got a population of 57k. It's arguably more recognizable than the closest major city (San Jose), which has a population of nearly 1 million.

The smallest Indian city that (almost) all Indians would know would be the hill resort of Shimla (pop 170,000). However, this is because a place is expected to have a population of about 100,000 to be declared a 'city', so for example New Delhi is only a town.