1. Getting an entity called "Province of Manitoba" incorporated as the name would possibly be rejected by a Secretary of State or Corporate Registrar in the same way the word "bank" causes similar trouble for non banks.
2. Unless there was a really good reason for naming the corporation Province of Manitoba, I think the SEC might get the impression someone was trying to pull a scam.
On the other hand there may not be a definitivelaw that forbids that conduct outright.