It's a case of the Latin transliteration not having a "natural"/intuitive pronunciation in English and hence a made-up pronunciation being used.[0]

I think that the transliteration itself was "correct" (assuming that the original Ukrainian was Палагнюк).

[0] https://chuckpalahniuk.net/author/frequently-asked-questions...

It's easier to just pick a varient which works in your new language. I've changed the pronunciation of my name because they Dutch have know idea how to pronounce it. They can't spell it either, however the phonetic spelling is close enough so I just let it slide. It's not worth getting precious when your name is unique enough.

Where did the "g" (г) go, Palagniuk seems closer (or Palagnyuk may be better?).

I know a little Russian, perhaps this is different in Ukrainian?

The Ukrainian г is pronounced as something intermediate between English hard "g" and "h" (ɦ in IPA)[0][1], so it's often transliterated as h.[2]

[0] https://en.wikipedia.org/wiki/Ukrainian_alphabet#Letter_name...

[1] https://en.wiktionary.org/wiki/ɦ

[2] https://en.wikipedia.org/wiki/Romanization_of_Ukrainian#Tabl...

There are no such cases. Everyone in the US is free to change their name if they're unhappy with it.