Pictures I've seen of pre-war cabooses show a simple "C. R. R. of N. J." painted on the sides, without any logo. The old "New Jersey Central" round logos are from long long ago, but I'd have to research the dates. The first 8-wheel CNJ cabooses date from 1902. The very first one built (converted from a SRRNJ box car) is 91155, in service on the Pine Creek RR at Allaire.
As built, the wooden cabooses had vertical tongue & groove siding, later replaced as needed with plywood. I would imagine the repaints after new siding would be simpler, leaving off the logo.
Quite a few rebuilds came after they started adding steel underframes in 1921. (Wood underframed units were class NE, after adding steel underframes became class NEa)
Most cabooses wound up being like George Washington's hatchet...two new steel heads and four new handles, but still his hatchet.
They tell me to act my age. I don't know how to do that. I've never been this old before.