James Lester unveiled the nameplates as they were reunited with the 34051 Winston Churchill.
The engine and its carriages are being restored for the 50th anniversary of Sir Winston's funeral on 30 January.
The restoration of the locomotive has been carried out by Mid-Hants Railway, Ropley.
The 34051 Winston Churchill, along with the Southern Railway's parcel van S2464S, which carried the coffin, transported the former Prime Minister from Waterloo in central London to his final resting place near Long Hanborough, Oxfordshire.
The carriage is being restored in Shildon, County Durham, having been loaned to the National Railway Museum by the Swanage Railway Trust in Dorset.
The train will go on display in the Great Hall of the National Railway Museum in York as part of its Churchill's Final Journey exhibition.
Mid-Hants Railway chairman Colin Chambers said: "All that remains is some additional varnish applied by our team of painters. It is planned to be on its way to York by mid-January."
Mr Lester said: "I'm so pleased to see the work on the loco is on track for completion by Christmas. This project has meant a lot to me as Churchill's Final Journey will not only tell the story of a remarkable man, it will tell the tale of many railwaymen who played a part in his last journey from the capital to his final resting place."
Sir Winston was laid to rest in the parish churchyard of Bladon, close to Blenheim Palace where he was born 89 years earlier.
A restored locomotive that pulled Sir Winston Churchill's funeral train has been unveiled by the fireman who manned the service in 1965.