No, that would give you the sort (using my own collection):
Louis Armstrong
Louis Jordan
Lynne Arriale
when what is wanted is
Louis Armstrong
Lynne Arriale
.........
Louis Jordan
(with lots of names between Arriale and Jordan, of course).
I have looked for ways to get OCD to sort with Last name First Name but display First Name Last Name for a long time (my first OCD entry is now 7 years old) and not found a way to do it. As far as I can tell, OCD will display in the left tree what it sorts by.
And, in any case, I do not think you can directly edit Primary Name. That is determined by what appears in the Artist Field on the general tab of an album's property sheet.