I’ve tested it, and ran across the same issue: only one material is available in Unreal.
It’s related to the obj file format exported from Rhino. If you still need to use the OBJ format for various reasons, you might need to “Organize objects by layer & material” in Rhino, according to this exporting guide:
You will export objects so that all objects on each layer will be treated as a SINGLE OBJECT in Unreal. This means that every object that will need a separate material or texture-mapping will need to be on its own layer in Rhino
Perhaps you can also play with the layer settings inside Rhino when exporting the mesh. I don’t have Rhino so I cannot test it out.
If you can’t solve this issue through Rhino, you could still import your OBJ in Blender (it’s free) & re-export it (either in OBJ or FBX), then bring it to Unreal.
However, according to the Rhino 3D doc, you can also export in FBX file format. Although the FBX version is not clearly mentioned (they are talking about version 6 and 7, but is it 7.0 or 7.5?), I would suggest to use the FBX file format instead, it’s a common standard used in the gaming industry.
Hope it helps.