Export *.3MF assembly with object names?

I’m looking at printing this model in full color and employees at Stratasys showed my how to verify / configure a print file in the GrabCAD print app. I was told I have to export an assembly.

My *.3MF file contains four parts so far. They overlap and the circled number under ‘Assembled’ are the priorities for each part.

It seems that Rhino does not export object names or block names with the *.3MF format.

Could Rhino somehow export blocks or nested blocks as *.3MF assemblies?
With object names and / or block names?

I found this document on the *.3MF format:

3MFcoreSpec_1.0.1.pdf (ctfassets.net)