If we pronounce all ending sounds according to Standard Grammar, it will be:
سيثٌ أمريكيٌّ لبنانيٌّ.
"siith(u) 2amriikiyy(un) lubnaaniyy(un)"
"siith(u) 2amriikiyy(un) lubnaaniyy." -- because of the full stop/the end of a sentence.
It is "-u" at "Seth" because the word is in the nominative case and is diptote which cannot receive tanwin and kasrah. (Some people say it is "-un", ie. "siithun", in the nominative so the word is triptote which receives tanwin and kasrah -- but, I think it is the weak opinion). So, if we hear -in, it is grammatically not correct. We can report it. :))