Yeah, pronunciation stays foreign in (almost?) all cases. We also don't make the r's pronunciation double in this case, although I guess most people would make the 'y' more Polish than English.
Dżelei is my original nickname (just one l), Jellei is the version for foreigners. So the first option.
Huehue, okay, thanks for telling me. I just remember seeing a book by Jennifer Niven written in Polish, and it put Dżennifer NIven, or something close.
Interesting... I'd give 99% that it must have been a joke made for some reason. With the name and surname of a real person - we just don't do that. Not in any serious context, at least.
Okay, that's not entirely true. Some important historical figures, mostly (although not only) from quite old times, have "Polish versions" of their names. Royalty usually does as well even if we're talking about contemporary royal families. Names that had to be transliterated from Cyryllic also have often have rather Polish then English versions (Nikita Chruszczow vs Nikita Khrushchev).
To put a few examples: Charles Darwin = Karol Darwin, George Washington = Jerzy Waszyngton, William Shakespeare = William Szekspir.
But even with those, Polish Wikipedia chooses "Charles Darwin" and "George Washington" to be the default options.