When you change your address you can click a checkbox saying you want a protected name/address. This means that companies that have you as customers/clients won't be able to get the new address, mail won't be redirected, etc
I did it accidentally during my last move and it was a pain in the behind
And it expires after a year by default so it feels rather pointless
If you own a danish domain name (.dk), unless you have protected address, all your info is a whois lookup away. Example lookup of ft.dk (danish folketing).
Domain: ft.dk
DNS: ft.dk
Registered: 1995-07-04
Expires: 2027-09-30
Registration period: 1 year
VID: no
DNSSEC: Signed delegation
Status: Active
Registrant
Handle: DATA REDACTED
Name: Folketinget
Address: Christiansborg Slot 1
Postalcode: 1218
City: København K
Country: DK
Phone: +4533375500
Email: webmaster@ft.dk
ID status: ID verified via electronic ID
Nameservers
Hostname: maleah.ns.cloudflare.com
Hostname: yichun.ns.cloudflare.com
This is why I've never posted anything from my own shitty website here. All of this is available from [myname].dk with my info on it. Also it's horrifying that our government is restricting access to its website behind fucking CloudFlare.
EDIT: I didn't redact anything from the lookup, this is the exact data I received.
I did it accidentally during my last move and it was a pain in the behind
And it expires after a year by default so it feels rather pointless