Asklemmy

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.

I guess the one that pretty much everyone knows in Germany is Buxtehude. It is being used as the poster child for a backwards town, far away from cities. Which is funny because neither is it backwards, remote or even very small. With a population of 40k it’s relatively large, compared to many other places in Germany, even just right next to Buxtehude. It is not far from Hamburg and its historic core is worth a visit. I think the name itself is the reason why it is being made fun of so much. Though there are so many other, much quirkier named towns in Germany but it somehow became Buxtehude.

Chicken, Alaska. Population: 12
I'd argue that everyone recognises "Chicken".

Fun fact: The settlers wanted to name their town "Ptarmigan" after the birds that were abundant in the area.
But none of them knew the correct spelling, and they didn't want to embarass themselves.

Gergovie. The place where we defeated romans 2000 years ago. Doesn't even exist anymore

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.

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.

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 there ☺️)

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.

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.

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.

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