Do you happen to have a citation on the fact that police officers can't run a license plate solely to check a person's name?
SHORT ANSWER: No....but read on
It is a complicated legal issue. Generally, police can run your plates for any legitimate law enforcement purpose. Therein lies the key. If police approach me while I'm on foot while I am conducting myself in a legal manner and I refuse to engage them in a consensual conversation (where they are going to try to find something with which to justify escalating to a detention), to then stalk me until I enter my vehicle is not a legitimate law enforcement purpose.....remember, I am conducting myself lawfully and they have not been able to find or manufacture RAS. With no RAS that I have done anything wrong, remember RAS is nothing more than reasonable suspicion that they can articulate to the court, the police would be conducting harassment, intimidation, and/or other unlawful action under color of authority.
Let's consider a lawful activity other than open carry. Let's say Officer Fife spots a particularly alluring member of the opposite gender. This individual is breaking no laws but Officer Fife wants her name and address in hopes of getting a date. Officer Fife approaches said individual who declines to talk with the officer. Rebuked and with his feelings hurt (or not) Officer Fife then follows the individual until they enter a vehicle at which time he runs the plates and obtains a name, address, date of birth, etc.
Officer Fife has violated the law in most states.
Now simple substitute the law abiding activity of exercising your second amendment for being the object of Officer Fife's desires. The situation does not change, only the lawful activity, and so the action is still an abuse of authority under color of law.