Vessel fabricated and shipped without nameplate

It seems that your vendor does not have a Quality Management System which is required by the codes (for pressure vessels). In this scenario, I would be suspicious about other things too. Assuming this is the only problem, I would ask the vendor to finalise their job themselves, including at site since they are responsible for the entire vessel with the name plate. You or your representative can be witnessing the job too.
If you or your qualified welder do the job you are sharing their responsibility.

However, if the vessel an ordinary non-code vessel with atmospheric pressure, of course, you can finalise the job after ensuring everything is in accordance with contract.

I've used option 2 in a similar situation.

I've used both options. Best to discuss with your AIA and they should give you guidance. They can also co-ordinate with the AIA at site to minimize the costs.