Probably Regina. And it’s famous for rhyming white schmamima.

Germany:

Bielefeld. Everyone recognizes the name, it's marked on all maps, officially it has a football club.
But in reality, it doesn't even exist.

Darwin, Australia.

Famous for being bombed by the Japanese repeatedly during World War 2

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.

In the US it must be Springfield because there's so fucking many of them that they ~~named~~ made a TV show after it.

Stupid sexy autocorrect.

Dildo, Newfoundland, Canada: 803 people as of 2021.

Someone here mentioned Vulcan, Alberta - however given the qualifiers of country and size, its 1769 people disqualifies it.

Also, though I am a Trekkie myself and know that Vulcan is well known in those circles, it's virtually unheard of outside them.

Meanwhile, Dildo:

https://www.cbc.ca/news/canada/newfoundland-labrador/odd-stories-of-2019-1.5389442

we have a town called "Fucking" with only a few hundred people living there. the town sign gets stolen once a month

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.

World recognition or in-country?

If world I'd guess Huskvarna (pop 24 000) for Sweden.

Known for having a company making chainsaws (among other things) named after it (Husqvarna). It is one of the two main brands of professional chainsaws (the other being Stihl).

Puerto Hurraco. Population 100. Everybody in Spain recognises its name because of a shooting that got burned into the collective mind.

Wales has St. Davids - population c.1,750

Roswell, NM comes to mind. Tiny and yet most people will think of UFOs when they hear the name.

In the UK it's got to be the City of London. Famous for being an ancient city established by the Romans and awash with history, now one of the world's biggest financial centers with a modern skyline of famously distinctive skyscrapers. It's home to some world-famous landmarks like Saint Paul's Cathedral and Tower Bridge, and has a population of about 10,000.

The City of London is not to be confused with London, London, London or London.