If the cat's name is "Kitty," then you would say "Kitty" in Spanish. If you know a Mexican man named Juan, do you call him John?
No, but if your name is John a Hispanic is likely to call you Juan.
Ever see a Spanish language newspaper? It's "instructive" in the way they think. In an American newspaper, we print the names of Hispanic people and places the way they say them. Buenos Aires is ... Buenos Aires, not "Good Airs." San Carlos is ... San Carlos, not "Saint Charles."
In a Hispanic paper (or telecast), New York becomes "Nueva York." Philadelphia becomes "Filadelfia." His Royal Highness, Prince Charles of England, is "El Principe Carlos."
Small wonder they expect to fly Mexican (or whatever Latin American country they come from) flags in the United States. They have what is sometimes referred to on the street as "an attitude."