Admittedly my WW2 history knowledge is quite lacking, but I don’t recognise Vichy because of the war stuff.

But I do recognise Vichy! Because we have a sub-type of mineral water in Sweden that is named after Vichy, “Vichyvatten”. Wikipedia tells me the original was from a spring near Vichy, hence the name.

Strong contender! Definitely less populated, but I think also less well known?

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).