Hi Terry,
What one does probably depends on a few things including what program one is using, how many people are involved, how many variable spellings of a name one has found, and perhaps whether one standard spelling exists in the present day.
I have many names with variable spellings (for one I've found about 90 different spellings and still counting).
I make a practice of recording each person's primary name under the spelling of the earliest record I have - sometimes that will be a birth certificate, sometimes a baptism, sometimes a marriage, etc, etc.
But I also record as a name variation in my program, every variant spelling under which the person has appeared - and that ensures that they will appear in an alphabetical list of people in my program under every variant.
Then I also add what I call an index name. For instance, for every person with the name which has the 90 or so variants (ranging through McLause, McLaws, Maclehose, Hose, Hozier, etc, etc - and with people chopping and changing throughout their lives), I also record them under the 'made up' name McLs.
That ensures that every person of this very variable name will appear in an alphabetical list of people under their primary name (which is starred in such a list) and under any variant names AND that they will also all be listed in order of forename under the 'made up' index name.
It certainly makes finding them much easier!
I follow the same system for other variant names e.g. Trippet, Trippit, Tripit, Trippett, Trippitt etc - as well as their primary name and any variants, I give them a 'made up' name of Trpt.
To each his or her own ...
JAP