You put the gears in, and your GCWR is "legally changed." No paperwork involved.
As long as your Suburban and travel trailer are properly registered based on what your state laws say, there is nothing else you need to do.
In some states the Suburban can be registered as a passenger vehicle. Otherwise it is registered as a commercial vehicle based on expected gross weight of the vehicle itself. That can be the GVWR, or something less than the GVWR if you never expect to be loaded to the gills, or something more than the GVWR (such as the sum of front and rear GAWRs). You don't HAVE to register at any specific weight, because you will probably never get weighed. If things change you can always claim ignorance and get off of any ticket by upgrading to the proper registration.
Trailers are also registered by weight. Usually the RV dealer will fill out the form at the trailer's GVWR, but again, it doesn't HAVE to be the GVWR. At least not in any state that I'm aware of.