I don't think there's anyone up there policing this, but I'm pretty confident that the consensus of the members would be that you should go with the records. If the records say Johann, then that's his name. With that said, I know there are a lot of cases where immigrants to the U.S. anglicized their given names or surnames or both, so there may be records over a person's lifetime that use different names. I have ancestors, for example, who were born as Johann or Georg or Wilhelm and died as John, George, or William.
It's your call as to how to best present the data in profiles you create, and you can use the nickname field, or free-form text in a Bio, to explain the usage of different given names. But there shouldn't be two different profiles for the same person because of a name change in any case.