Unfortunately, we don’t have functionality to attach Revit parameters onto Blender objects out of the box. Just simple properties that are directly on the objects themselves.
However, @gokermu has showed off a way to pick certain Revit Parameters and attach them as Blender properties via a simple python script that can be added as part of the receiving process in Blender.
With a few tweaks, you can use this script to attach the properties you care about to the blender objects.