Yes, though O’Brien is Ó Briain in Irish, according to Wikipedia. I think the apostrophe in Irish names was added by English speakers, perhaps by analogy with "o'clock", perhaps to avoid writing something that would look like an initial.
There are also English names of Norman origin that contain an apostrophe, though the only example I can think of immediately is the fictional d'Urberville.
There are also English names of Norman origin that contain an apostrophe, though the only example I can think of immediately is the fictional d'Urberville.