Article 2-A.2.2(a) provides for a Professional Engineer registered in Canada or the US AND experienced in pressure vessel design. There are also options (b) and (c), depending on the jurisdictional requirements of the location where the vessel is to be installed - per 2-A.2.3.
I note that your original question relates to whether the manufacturer can certify it. The answer to that is typically no. The purpose of the UDS is provide direction to the manufacturer for how to design the vessel. Since this document is for the benefit of the ultimate User of the vessel, the closer the author, and ultimately the certifier, are to the User, the better. Also note the last sentence in 2-A.2.1(a).
This document should not be considered just a "document" that needs to be checked off in some inane compliance verification. It forms the heart of the engineering specification for the engineered vessel.