Either way, the official apps that let you check the record do not allow tracking, only verification. The simple solution is that if you don't see them using the official app, simply leave.
So why are name and date of birth included in the QR code?
It'd be easy to make something that looks like the official app but does store the information, especially if that app is open source (is it?).
Basically even if they collected the data they wouldn't be able to use it. If they just collected your name to personalize your experience they'd be literally in deep shit if someone asked: "where did you get this information from?" - which to you may sound a weird question, but since 2018, at least in my country, more and more people ask this question.
When in doubt, report. They'd need to show to authorities that the person gave explicit consent to store that data and to be used for personalized experiences.
It's about consent. If the user didn't give consent you have no use for the data, and you'll be storing toxic material to get you fined.