My understanding from talking with some people of the family name 박, as well as studying some history of Koreans in the U.S.A, is as follows:
When Koreans began coming (primarily) to the United States, they were of course asked to register their name with the immigration officials. When 박씨 Koreans were asked their name, they likely responded in one of several ways:
- "My name is 'Pak'" (with the actual Korean pronunciation). The daft American then hears "Park" (we are manytimes talking about New Yorkers here; R is silent to them half the time anyway. See this link also). The immigration officer decides to write the name as "Park," since that is what he heard. As silly as this sounds, consider the fact that most non-Koreans are pretty bad at hearing Korean and properly tranlitterating it into roman letters. Say "park" with a New York or Bostoner accent and it actually sounds quite close to 박 I feel. Immigration officials back in the day were nortoriously bad at properly spelling names. They many times opted for strict phonetic spellings or simplifications of foreign names.
- "My name is 'Pak'" (with the actual Korean pronunciation). They then get asked how to spell their name. (I even get asked this all the time by non-Korean speakers for Korean words). There is a complete ignorance about the fact that not every word in the world is spelled in "English." If the Korean 박씨 manages to come up with a spelling like "Pak" or "Bak," they still eventually run into people calling them "Pack" or "Back" and decide they would rather be called "Park," since it at least sort of sounds like their name. And sometimes you would rather have control over how people mispronounce your name than to leave it up to chance. No English speaker over the age of 3 sees the word "park" and butchers its pronunciation.
- "My name is Park." In an attempt to match their name to an "American" name (or avoid the pitfalls of #1 or #2 above), these 박씨s conciously take on the name "Park."
Ultimately, I think that the "Park" name for 박씨s comes from a mix of American ineptitude at the immigration level to properly transcribe a person's name and Koreans desiring to have a more "American" name. The closest word in English to 박 would probably be "pock." But who wants to have the nickname Pock Mark? Or open themselves up to jokes like "Mr Chicken Pox (Pock's) car"? Hence the choice of the name "Park."