'Tommy' was an abbreviation of Tommy Atkins, the fictitious sample name on WW1 army recruitment forms, which in itself came from the initials T.A. of the British Territorial Army, then being sent over to help France and Belgium..... or so I believe.
I suspect a 'Long Tom' is anything longer than the norm.
I'm afraid that that doesn't fit the facts. As has been alluded to, the Territorial Army was not called that until 1920.
And, again as has been said, we don't use the term Long Tom over this side of the pond.