From comments in the G2G Forum about where an event occurred that state one uses the locale "at the time the event occurred" rather than any later legal adjustment through re-drawing of boundaries, I myself my opinion only would suggest that any of the variations in the SPELLLING of the name are made a note of in the Biographical section.
WHICH name you actually chose as to spelling would depend upon the one most used by the person you are profiling. BUT THAT is my opinion.
I have seen various researchers make those notes. All too often the surname is spelled differently on the marriage license, the marriage record, in the birth record / baptismal / christening certificate, in legal documents, and so forth, as you have noted yourself.
For instance I've seen Speer, Spier, Spear, Spears and have no idea which is "correct" but I went by the records, making note of the variations. The one I picked to use as the LNAB was the one most often cited (spelled out).
HOWEVER, someone else there at WT may have a more informed idea or procedure.