Generally, it is more efficient to have one large than two small devices.
The twin fan solution not only needs a gearbox and driveshafts that a single fan solution does without, it also has more intake and nozzle surface area per cross section than the single fan. This will cause more viscous losses and lower efficiency. The only advantage would be if size limitations make a single fan impossible, but in that case it would be more straightforward to have each fan driven by its own core engine.
Famous examples of aircraft which used a single engine and two "fans" would start with the Wright Flyer models, all of which had a single engine drive two propellers via bicycle chains. But the list is short.
The list of opposite designs where two engines would drive a single propeller or fan would probably be longer, and my favourite from this list is the LearFan.