If Renegade Doppelganger becomes a copy of another creature, that doesn't count as having a creature enter. Renegade Doppelganger was already on the battlefield; it only changed its characteristics. If Renegade Doppelganger gains any "enters" triggered abilities, they won't do anything. The same is true of any "as [this creature] enters" or "[this creature] enters with" abilities.