On the first issue. Having a database association between a car registration and known or even likely drivers is a relatively trivial exercise in associating different databases... namely car registrations and licenses. Shared address would be the simplest way to associate cars and possible drivers. But that would clearly not be 100% reliable, so it would be merely a convenience for the police so they don't have to manually enter information for writing up a ticket or checking for outstanding warrants. Actually, it could be of added benefit because it could end up bringing up information on other household members who may very well be in the car at the time.
The only concern about making up a name that would be valid is if the courts saw making up a name or withholding your name as a valid exercise of your first or 5th amendment rights. Otherwise you could simply make it a requirement for drivers to give their real legal name to police and it would be practically no different than presenting a fake ID or refusing to give your ID to the police. And the benefit is that such a system would eliminate the possibility of people getting cited for driving without a license just for forgetting their license at home. It is a real shame that in most states the system has made forgetfulness a misdemeanor. I know that I have left my wallet at home probably half a dozen or maybe a dozen times over many years and driven my car, thankfully never got caught.
As for the ID being a convenient way to get started for looking up someone's data. I don't dispute that. Especially, for all those scenarios where someone has a hard to spell name or like you mention a hard to facially recognize face. Having a card with a name, picture and bar code on it makes some sense. And there are many many somewhat artificial reasons that having a physical ID makes sense. Like access to Federal facilities requiring a REAL ID compliant state issued picture ID. So I wouldn't argue for a wholesale overnight change. But I do have a concern that most states have laws on the books that make a simple and reasonable act of forgetfullness a misdemeanor crime.
I think what I would suggest as way to make the law less unnecessarily onerous would simply be to allow people to avoid an additional citation for driving without a license if the police can verify your identity via other means and can verify that you do have a license to drive. So simply eliminate the misdemeanor for those who have merely forgotten their licenses as long as the police system is working.