In Italian, "troia" means "whore", as well as the ancient city of Troy. Italian uses "ina" or "etta" as diminuitive suffixes, rather than the Spanish "ita", but still... I don't know that I'd want to be discussing it at work.
And we (italian) speak about the city of Troy without any shame because has a completely different meaning, so I don't see any problem in speaking about Trojita at work (which is also a nonexistent word in italian, opposite to the translation of Troy)