I don't think US Government is the main worry to be honest. They are too inept to actually pull off a large project like that - they can't even keep bridges up or the price of stamps down. It's the same, but now larger and less efficient, government that knew enemy planes were approaching Pearl Harbor, but was so inept as to be unable to communicate that to anyone that mattered. In the USA, I'd worry much more about credit agencies and similar services, who, unlike the government, basically have free reign to share your history with whoever wants to pay them.
I worked doing people identification for government. I see getting chips implanted about as likely as the US returning to the moon.
Besides: They already have your history, including your past name. It's available in numerous government databases, no matter how careful you were, at least if you ever received any government services and kept receiving them (such as mail, social security card, driver's license, any public assistance, dependent of a government worker, police contact, car license plates, attended college/got a degree, applied for federal student aid, bought a handgun, filed taxes, have a kid in school, crossed an international border, have ever had a hunting/fishing license, etc). Even for changes like birth certificate corrections (not changes, but actual corrections where a new birth certificate is issued), I'd bet anyone $100 that they keep an "audit log" of all entries/deletions/corrections/etc that is generally not available to the public, but is available internally within the agency (if for no other reason than to keep staff from creating themselves 20 dependents on paper). The only thing that allows stealth today is that most of these government workers actually follow the laws that protect that data. But all it takes is one that doesn't. Most people aren't going to have the ability to disappear (at the very least, most people today are going to have social security cards and will seek to correct them rather than illegally establish a new social security account).
I do think everyone should care how these government agencies combine data between databases (what are the consequences, for instance, of tying child support databases to hunting license databases, for people who are trans? I have no idea, but I'll bet there is some consequences). And we should be concerned about what data the government has - particularly how long they keep it. Is there any reason to keep a record that I had a fishing license 10 years ago (remember, you probably showed a driver's license number or gave a social security number - which can be tied to your current records)? As systems have went to computers, the common trend is to keep data forever, as it's cheap to do so now (vs. paper records which were a pain in the rear for agencies). It's a lot easier to get outed than it was 10 years ago.