Dozens of stories go about that couple of foreign tourists, lost in Firenze, desperately looking for “Florence”. It’s an old joke, known in many different variants: sometimes they are in Venezia, looking for “Venice” or in Napoli, searching “Naples”.
To be honest, I have never had this kind of experience: all the tourists I met in my career were smart people, and they knew that “Mantua” was the English name of Mantova. But quite often they asked me what was the right name of the city. Of course you can use both of them, since “Mantua” is the exonym for “Mantova”. And “Mantua” is the word used also in the local dialect and in Latin. So, don’t worry: you can not go wrong using it.
Another frequent question is about the reason of this… in general, many people wonder why the name of some Italian cities are translated in English.
You can find many posts about this topic on Tripadvisor’s forums. And many people blame it on the colonialism of the British Empire.
Actually it has nothing to do with British colonialism... It started centuries before. For example Shakespeare mentions the city of Mantova using the name "Mantua".
The reason is that – during the Middle-Ages and the Renaissance – many diplomatic links have been bound amongst the powerful Italian city-states and foreign countries, so the names of the historic Capitals of the Italian states started to pass the borders, being changed according to the languages of the different countries.
If you notice, for example, only the cities who were VERY famous during the Renaissance have a 'foreign' name: Florence, Milan, Rome, Naples, Mantua, Turin, Venice, Syracuse.
Due to their past glories, all these cities gained the honor of an exonym. And - in my opinion - in sign of respect to history, it is right to use it. A nice way to pay a tribute to the past glories.
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Here’s a list of the main Italian exonyms
Florence - Firenze
Genoa - Genova
Leghorn - Livorno
Mantua - Mantova
Milan - Milano
Naples - Napoli
Nursia - Norcia
Padua - Padova
Rome - Roma
Sienna - Siena
Syracuse - Siracusa
Trent - Trento
Turin - Torino
Venice - Venezia