passengers from liverpool to u.s.a

I know my great great grandfather travelled from hull to liverpool to board a vessel bound for u.s.a. He took some of his children with him and left the rest behind. He was from Hull and his name was train. We think he changed or it got changed to Trainer (or Trainor), when he entered the U.S? It would be somewhere around 1830's 40's. Iam sorry but that is all I have to go on. Thankyou Chris Hoff-Yorkshire chris hoff