There are alternate spellings because records clerks had issues or did not care. There are alternate spellings because your relative could not read or did not care.
But then there are those individuals whose last names are, for the most part, spelled consistently–this is more often the case the more recent the relative.
Various members of my Trautvetter family used other renditions, particularly Troutvetter and Trouftetter. I don’t correct the spelling of the name if they used something else. Christian Troutfetter, who went to Kansas used Troutfetter in virtually every record and signed his name that way in every handwritten signature I have for him (and it’s how the name is on his stone). His descendants use that spelling to this day. Another member of the family used Troutvetter fairly consistently, including having it put on his stone. His descendants use that spelling to this day.
I don’t refer to Christian as Christian Trautvetter–I refer to him as Christian Troutfetter. The same for the other relative. I use the Trautvetter spelling for members who used that name or for relatives who have so many variants that I can’t tell if they had a preference.
Documents are transcribed as written. It is when I’m writing about the people that I have to “pick a spelling” if there was not one used a majority of the time.