Kittleson

Hello, I am just starting out on my family tree quest and have hit a snag. In our family we have the perverbial 'our name was changed at Ellis Island story' which has been debunked in two different ways. My family Kittleson came over between 1860-1862 and according to this site more than likely went through Canada. Plus Ellis Island asserts that they very rarely changed names. So my question is how do I find Kittleson if they were Haave? If there were no records kept in Canada at the time what then. My direct ancestor was Gullick Kittleson. His wife was Sarah and they had a son maybe 4 years old at the time of crossing named Henry. They may have traveled with Gullicks brothers Kittle, Halvor, and Ole and thier family's. I don't know what the name Haave means or where that came from, perhaps a farm name? That and Gullicks father was supposedly named Ole so why wouldn't we now be Oleson's? If anyone can clear any of this up or point me in the right direction it would be greatly appreciated.