Says who? Where did you get this information?
Assuming this is true, it would be easy to make this ID totally anonymous. Just text and a bar code indicating "cleared." It might include a serial number which is anonymous to anyone without access to the database. There would be no need to include the name. It would resemble an "I VOTED" sticker, or a marked ballot, which is secret and anonymous. (Which, by the way, is why it makes no sense for the Trump administration to claim they might change the election outcome by finding illegally submitted write-in ballots. You can't tell which is which once they are removed from the envelope. You can only do the entire election over again.)
Some number of people would probably get fake tags to avoid having to get a vaccination. This would be a very small threat to the public. Really nothing to be concerned about.
Once herd immunity sets in and the number of cases begins to fall rapidly, there would be no need for the ID. We would toss them all out.
A few years ago, someone suggested that if self driving cars become common, it would be good idea to issue RFID (IFF) radar response tags to people. Someone immediately responded saying, "no IDs! No government tags!" This is a complete misunderstanding. An RFID tag would not identify you personally. It would only tell the automobile radar: "Human being here! Moving object! Watch out!" Actually, it might not even say "human being." I suppose people would put the tags on dogs, baby carriages, bicycles and so on. I doubt the issuers would bother issuing separate tag types for each category of these objects. These tags would cost a fraction of penny each, so you would put them in your wallet, overcoat pocket, key fobs, winter gloves, and whatever else you felt like. Having two or three on you would make no difference. Maybe put one on the mailbox or a tree near the road.
He was being facetious, I hope. Jezz Jed you crack me up. Sooooo serious. Thanks for my morning belly laugh.