Name changes with emmigration!

I have been trying to track some of my grt grandfathers, brothers family who emmigrated in aug 1888, april 1882, february 1893, and may 1887. My problem is that I have them as leaving, or boarding as Kristofferson Ronnei's or Chrisofferson Ronneids, as there last names and farm names. So, what would they use in America? Would it be ronnei, ronneid, christofferson, kristofferson. How can a I determine this? Any helpful hints to this would be greatly appreciated. Yours truly puzzled, riggs.[?][:)]