that's called a close coupled sedan/coach and the fitted trunk is the fore runner to the trunk built in. The body appears to be shorter to accommodate the trunk. Sometimes you see these with a special small luggage rack attached to the back panel of the trunk.
I do not know what the correct Chevrolet FISHER BODY model number is. This was used on 1933 master series and 1934 master series . I know I have seen a few 34 masters made into street rods back in the 1970--1980 era.
mike lynch