The Hazardous Materials Regulations of the USDOT/PHMSA require the person who offers a hazardous material for transport (i.e., the shipper) to mark the package with the name and address of either the consignor or consignee except in certain specified circumstances. You can read all about this general marking requirement of 49 CFR 172.301(d) here:  The Name of the Consignor or Consignee as a Marking on a HazMat Packaging.

When required, is it acceptable for the address to be a post office box instead of a physical address?

Yes.

This USDOT/PHMSA letter of interpretation makes it clear:  03-0156.