The Flying Scotsman

That will be "Flying Scotsman" then.   "The Flying Scotsman" is the name of a train, recently reintroduced on the East Coast Main Line. Locomotives do not have "The" in their names.

The comes in when it has the carriages on the back with passengers , on its own with the tender its Flying Scotsman .

That would only apply if it was hauling that particular named train service.  At present it seems to be run using electic multiple units.

So you actually get two of them - the locomotive and the train.

Actually it is not an electric multiple unit there is a locomotive class 91 (normally at the north end) a rake of mk iv coaches with a driving van trailer (dvt) at the other end, the northbound,"The Flying Scotsman" was in the past the 10.00 am from platform 10  at KX,It has at times also been formed of an HST set