That's not the reason why Popes change their name. Peter's name was changed from Simon, but most of the Popes from the first millennium of Christianity kept their baptismal name upon becoming Pope. The first one to officially change it was Pope John II. His birth name was Mercury and they thought it was inappropriate for the Pope to have the name of a pagan god. It didn't become the norm to change the name until 400 years later, and even then, there are two Popes in the last 1000 years who kept their baptismal names anyway. Pope Marcellus II (born Marcello Cervini degli Spannochi) in the 1500s was the most recent to break the tradition and keep his baptismal name. Any Pope could choose to keep his baptismal name, but I'm glad this guy went with Pope Francis and not Pope Jorge or Pope George or whatever.
>> My question is why he is designated Francis I? Just plain Francis should be sufficient until there is a Francis II. <<
I agree. Looking at other Popes to have a new name, I see they're listed as Pope Linus, Pope Zephyrinus, Pope Fabian, Pope Liberius, Pope Lando, etc., I see they're listed simply by their papal name in lists of Popes, there's no "I" added to the end of it unless someone else takes the same later on. (i.e. Pope Celestine was retroactively listed as "Celestine I" when Celestine II became Pope). Odd thing, I think Pope John Paul I was officially called "John Paul I" before John Paul II was elected. I'm not sure what the rules are, given that Pope Francis is the first brand new for a Pope in 963 years (Pope John Paul was a combination of his two immediate predecessors -- John XXIII and Paul VI). I would prefer the media just call him "Pope Francis" myself. "Pope Francis I" when there's no second Pope by that name looks silly, especially since there may never be a Francis II. I don't think anyone is going to be confused and think there was a Pope Francis before this guy.
>> In South America, at least in the Spanish-speaking countries of that continent, he is known as Francisco Primero. (Remember, he is Francis the First, not Francis One.) <<
That's another odd rule. When I took Spanish in 7th grade, the Spanish teacher had all our birth names latinized to the Spanish form, or found a similar-sounding Spanish name to call ourselves in class. Thus, my name was William and I went by "Guillermo" in Spanish class. I was later told as an adult that that's not appropriate to do in Spanish countries (refer to yourself as the Spanish form of your name), and that Bill Clinton would still be addressed as "Bill Clinton" in Mexico, Johnny Depp is still called "Johnny Depp" by Mexicans, etc. But then I found out the artist Michelangelo is referred to as "Miguel Ángel" in Latin American countries, John Paul II is "Juan Pablo segundo", etc. Can someone please come up with a consistent set of rules for when names from other cultures should be altered to the native language? It seems so random.
The rule for what someone will be called in a Spanish-soeaking country is similar to what he would be called in an English-speaking country: a person’s name usually is kept the same (although a local nickname may develop), but for historical figures it is usually translated (e.g., Cristoforo Colombo is Christopher Columbus in English and Cristóbal Colón in Spanish), likely because names were translated to the local language back in the olden days. It is also always translated in the case of popes (instead of using the official Latin name), and is often translated in the case of foreign royalty (probably a remnant of the den days—if Queen Elizabeth I was known as Isabel I in Spain, why wouldn’t Elizabeth II be known as Isabel II?).
As for your Spanish class, the teacher probably gave all the kids Spanish names so that you all would practice pronouncing names in Spanish.