Question: I'm planning to travel to Costa Rica soon, and I hope to get a chance to find some people I can practice talking Spanish with. Do you think it's better to introduce myself using my English name (Jim), or should I use my name in Spanish (Diego)?
Answer: I can't tell you what the etiquette experts would say, but I can tell you what my experiences have been traveling in Latin America. I've often introduced myself by both my given name (Gerald) and the Spanish version (Geraldo, which isn't a common Spanish name and isn't instantly associated with a celebrity). I'd say that usually, probably about two-thirds of the time, people have then called me by my English name, or at least they tried to. They had trouble pronouncing the initial sound (which is the same as yours), so it would often come out sounding like Yerald. Your name will probably end up frequently sounding more like Yeem than Jim.
If you'd rather introduce yourself by one name or the other, and you can handle hearing your name mispronounced, I'd suggest just using the name you use every day. Most Latin Americans (Spaniards, too) are familiar with American TV and movie celebrities, so they're used to hearing and even using English names. In some areas, it's trendy to give children English names of certain celebrities. And if your racial background and/or clothing are such that you look like a foreigner, they probably won't be expecting a Spanish name anyway.
Also, it might be worth noting that the Spanish-language media refer to foreigners by their foreign names. U.S. President George W. Bush was known universally as George W. Bush, not Jorge, the Spanish equivalent, for example.
Interestingly, though, famous historical characters don't necessarily get the same treatment. The first U.S. president is referred to as Jorge Washington as often as not, and the famous playwright is sometimes referred to as Guillermo Shakespeare. I suppose we anglophones do the same thing, using the foreign names of modern-day foreigners but anglicizing the names of some historical figures. The famous 15th-century explorer is known to us by the anglicized name of Christopher Columbus, for example, not Cristóbal Colón, and the Spanish saint known as Santo Domingo in Spanish is St. Dominic in English.