Mathematica, a program I use, can access various databases including of countries and cities. There are 240 countries in a database (and more than 160 thousand cities) which makes 240 * 239 / 2 country pairs, or nearly 30 thousand of which 95 % don’t share a single city name. The other 5 % do, France and Spain for example have 54 city names in common, like Avion.
There is one Avion in France and one in Spain. There are more instances of London: four in USA, the one in England and also one in Canada and one on an island in the Pacific Ocean. Existing in four countries doesn’t break the record though, that is held by San Lorenzo, Santa Maria and Santa Rosa which each name a city in 13 countries. Santa Barbara, Alexandria and Victoria also can be found in at least 10 countries.