Long Tom is a Name that was used on Steven single barrel shotguns sold by Sears and Roebucks in the first half of the 20 century, but alas, it is one of the names that is being tagged on any long single barrel shotgun, so no harm done.
Do you have a serial number for your shotgun? However 36 inch barrel may be unusual but the Blue Book ( last years ) list the 370 at 120 dollars in 100 percent condition, in the well worn and used condition most of the guns are in the value gos down to 70 dollars. At one time the factories were very accommodating and would fill any special order within reason. The 36 inch barrel may have been a special order but it does not appreciably increase the value