I would start by making sure they used that name across time, for example in multiple census and vital records. That way you can determine it was a change, rather than a census takers error.
I would then list only those family members with that spelling, and the others with the spelling you are familiar with. For example, one of my relatives changed the spelling of his birth name McNamara to MacNamarra. None of his siblings used that spelling. So, I changed his and his sons names to that spelling, but not his siblings. I used the McNamara spelling for his father. You can always use both for that person as well, and put a comment about the use of the name. However, I would not add the alternate spelling to all people in the tree. Clear as mud?
You can add both spellings to the name of your tree, and use both when you search.
Also, people did not always have to file a new name change with a court, it was often enough to just start using the name on documents.
I don't use Family Tree Maker, so I can't comment for sure on the technical part of your question. I think you could put the last name, then a / then the alternate spelling in the last name section. The software I use has an option to add an alternate or AKA name.