In the USA, came from the UK which was known (in the 1700's) for having secret trials, secret evidence, secret witnesses, and secret punishments. So the founders built this system to be transparent in many ways. And that meant public recording of crimes. Fast forward a few hundred years, and this computing thing takes off, and records everywhere are put in a system and easily searchable.
Having the secret system in place in the Netherlands and the transparent/easily searchable system in the USA don't really mix all to well.
(Admittedly, much of the courts systems are still opaque as mud, but some important parts are constitutional - like seeing/questioning witnesses, jury of your peers, etc)
I imagine if you have a valid reason and petition the court you can have the identity revealed?
For some people and some cases this is not possible. Sometimes there is a publicly known person involved, like the case of Keith Bakker which is in the Dutch news today. He has been a lot on TV in the past. Another case was the killing of Pim Fortuyn, a well-known politician, where everybody knows the name of the killer and he is now somewhat forced to live in another country. Mostly the news talk about Jos B. or similar semi-private namings. People closely involved know who it is about, but it doesn't need to be on TV or in the newspaper.
About your other question though: one of the courts states in an answer to one of their frequently asked questions, https://www.rechtspraak.nl/Organisatie-en-contact/Organisati..., that a copy of a verdict will always be anonymised. No suggestions are made for when you want to apply for an exception to that rule and I suspect it is not possible at all. I am also struggling to come up with a valid reason for such a request; if it is indeed impossible, that might not be a problem.
Example: I own and live in a condo apartment in a housing complex where the legal entities for my building and four other buildings are all members of one overall legal entity for the complex. Some of the other legal entities, and some of their administrators, are currently suing the overall legal entity with various claims. The management notified all owners that this was happening, as they're required by law to do, but didn't give the full complaint. (They did name the individuals and legal entities who filed suit, including the administrator roles of the individuals.) I'd like to read the full details.
Where I live, I can go to the public library or the courthouse, search for the involved parties in a database, and read the specifics. I don't have to prove that I am indirectly a partial owner of the entity being sued (though I am); this is available to the general public.
How would this work in the Netherlands if public access is anonymized?
Criminal status is protected.
So if you're 22, the crime you committed when you were 19 won't count against you, but when you turn 23, it starts counting again?
This leads to the odd scenario where someone born 16y364d ago can get it on with someone born 16y363d ago, then the very next day it becomes illegal, and the day after that it becomes legal again.
And what kind of results do they get? (I'm genuinely asking)
Any time I hear about a "you can apply for X" series of bureaucratic hoops one can jump though I can't help but wonder if it's like getting a building permit in SF or a handgun license in NYC where only the people who've made the right donations to the right people can get what they want and everyone else gets the bureaucratic run around.