In other areas besides aviation, engine identification is defined by what the motor trade defines as a "short motor". This is the basic engine - the block, crankshaft, bearings, conrods and pistons and rings - but no head or heads, or any engine accessories.
When you purchase a reconditioned short motor for a road vehicle, it comes with a new engine serial number and that new S/N has to be advised to registration authorities.
However, aviation rules and laws operate in a substantially different fashion to the rules and laws of road vehicles - and I would be very surprised if an aircraft engine manufacturer would accede to a request to fit used accessories to a completely new engine block, and then be expected to certify that engine fitted with used accessories, as a complete brand new engine.
For aircraft, engine accessories are regarded as critical engine items, with an operating lifespan that is in line with the major engine components such as crankshaft and pistons and rings.
Thus, fitting a used carburettor or a used starter motor to an otherwise new basic engine would be viewed as on a par with fitting used pistons and rings, and the engine would in no way be viewed as befitting a new engine data plate.