I think you guys are getting a little too philosophical.
The Sith and Jedi orders are nothing more than organizations made up of certain individuals.
As long as other members of the organization recognize you to be one of them, you are a Sith/Jedi. Alignment has nothing to do with it.
Of course, if the other Sith actually KNEW you are secretly following the light side, then they'd probably kill/banish you, but as long as you manage to prevent that, you are a Sith.
This. It goes both ways. A dark side Jedi is still a Jedi because he/she has not joined the organization formally known as "Sith." If said dark jedi is banished however, then he/she is simply exiled from the order, they will not be considered Sith unless they join their ranks.