Census records are notoriously inaccurate - the process of obtaining the information and the purpose of the data collected allows for plenty of minor or major errors. Names in particular were frequently misrecorded because the intent of the census is for demographic purposes - the exact spellings or order of one's name was/is not of vital importance and therefore it is quite common to see misspelled or flip-flopped names. It does not necessarily mean the individual would flip-flop their names in practice, just that they were recorded backwards.
However, some people did go by their middle names. I have more than one "John Henry" in my tree who clearly went by "Henry" or "Harry" and their first name can't even be found on most censuses.