I prefer the one of the ideas suggested earlier. I think it would be best if every religion HAD to have at least one sect/cult/denomination. This would ensure that all Temples, priests and commoners are a part of a sect and make the dividing line clear in the case of succession.
When a religion is created it comes, by default, with a default sect/cult/denomination So if I create the religion "Nomonisim" it would come with a sect/cult/denomination I might call "Orthodox Nomonism." When someone joins the religion "Nomonisim" they are automatically a part of "Orthodox Nomonisim" as it is the sole sect/cult/denomination. All temples built are dedicated to "Orthodox Nomonism" for the same reason. All commoners converted by priests or Temples of "Orthodox Nomonism" are a part of that sect/cult/denomination.
A while later a priest chooses to create a new sect/cult/denomination of "Nomonism" called "Jestaric Nomonism" He is the only member. At this point all members of "Nomonism" are informed of the new sect and its unique beliefs. All members of "Nomonism" can freely choose to dedicate themselves to any sect/cult/denomination within a religion at any time. A lord can choose to rededicate a temple to and cult/sect/denomination of "Nomonism" at any time (At a cost perhaps?). When new players join the religion, they are given a choice as to which sect/cult/denomination to dedicate themselves.
Commoners could just see a religion/sect combination as separate religions. If an "Orthodox Nomonism" temple has been a region for a while, all the peasants converted will be "Orthodox Nomonists." If the region Lord then dedicates the temple to "Jestaric Nomonism" the peasants will slowly be converted from "Orthodox Nomonism" to "Jestaric Nomonism." Commoners converted by an "Orthodox Nomonist" priest would be "Orthodox Nomonist" until they are converted by a temple/priest of another sect/cult/denomination or another religion.
At this point every temple, player and peasant will always be of one sect/cult/denomination or another. If a sect/cult/denomination succeeds from the main religion to become it's own, independent religion, whatever is aligned with that sect/cult/denomination at that time comes along. That is it!
I would think that a sect/cult/denomination could be started by any priest of the religion. Each denomination could have it's own ranking of priests. Only the highest ranking priest of a sect/cult/denomination could initiate a succession. When a priest changes from one sect/cult/denomination to another, heir rank will be determined by the leaders of the sect/cult/denomination they switch to. They are, after all, saying, "You guys are SO right. I submit myself to your teachings!" As an example, if an Elder Priest on "Orthodox Nomonism" decides to join "Jestaric Nomonism," his rank in "Jestaric Nomonism" would be determined by the priests of that sect/cult/denomination. They could decide that the former Elder is nothing more than the lowest priest of "Jestaric Nomonism." They could make it a lateral transfer. It could also be a promotion. I can see the benefits of recruiting a respected member of another sect/cult/denomination. Promotion/lateral transfers could be a part of the negotiations leading up to the transfer.