Interesting. I was just looking at Printful, they do printing and fulfillment, and chatted them to ask whether they relabel (they do, sorta) and whether they use their own RN# or should I use mine (as a designer/customer). The guy didn't even know what I was talking about. "Is that industry standard?" etc. And he insisted that all the legally required info is on the tags they DTG onto the shirt, which does not include an RN#. So... they don't use RN#s at all when they relabel.
The info I was trying to glean, though, is... if I am a relabeler, do I use my own RN# or do my customers (the designer/marketers) need their own? Or do I use the print shop's RN#?