I wouldn't think that the Census would be a reliable source for spelling of one's name -- last or otherwise.
Census takers are generally spelling (or misspelling) from what they hear, or think they hear. And they may not get their information first hand either (maybe from neighbors, or other family members).
Other government records might prove more reliable for name spellings, birth, death, military, etc. -- yet there can be errors in those as well, and often for similar reasons.
The best source is from the person themselves, if they can read and write. When they write letters, or sign documents, etc. Of course, these are the most difficult to find.
Often, you just have to make your best guess, based on the available sources you have at the time.