Not sure how to correctly write this - as one word, separate? Do I retain the apostrophe?
Usually the apostrophe in personal names retains, so we have in translation Юджин О'Нил, Шакил О'Нил and actually a lot of other
О'Нилs. The same about Жанна Д'Арк (or д'Арк) or Габриеле Д’Аннунцио (or д’Аннунцио) etc.
This is what you'll see in newspapers and books. In official documents it could be more tricky though. I won't be surprised that there are no regulations about this particular case so say some O'Neil will decide to become a Russian citizen he can be written just as О-Нил or О`Нил. Bureaucracy is a bureaucracy so I can imagine some stubborn official (check out for instance, this post) - but this has nothing to do with Russian language, so let it be )