For all alternative spellings of a surname, they can be entered into the Other Last Names box - so that they show up on the profile as AKA names. If a person used several different spellings in various records then we need to provide a record of those names.
If any children were given a different spelling from the parents, then the childs surname must be listed as spelled on the record - usually the birth certificate. And again any other spellings or names used by that child, are to be entered into the Other Names box.
The Current Name box usually has the spelling that was used at the time they died.