> Does the full name have to be your legal name?

Pretty much. Only your person has rights, not the fake identities you created. They can actually request a copy of an ID or something comparable to confirm your identity. You might have a hard time removing your data, in some cases, when using fake names since then your identity can't be confirmed.

> Only your person has rights, not the fake identities you created.

But if they only know u/lucb1e to own +31612345678, then it's all good and well that you're requesting data as Luc Lastname but that's not going to match their records anyway; that doesn't prove you're the legitimate person to send this data to.

> They can actually request a copy of an ID or something comparable to confirm your identity.

When I called the Dutch DPA about this, specifically about MAC address tracking (I got an email "welcome to ikea!", sent to anothercompany@lucb1e.com, when I connected to ikea's free wifi), and they said that supplying the MAC address is the identifier to use because that's the only thing they can match anyway. This was in 2018-ish so I may misremember details, to be fair.

As far as I know, this is similar to copyright under a pseudonym. If you can't prove it's yours, sucks, but if you can, then your rights are yours to exercise.

Yes, and unlike a sign up for a random site, you are actually stating the info and signing the form, it is as "official" a document as a non-notarized/non-certified one can be, there could be (improbable anyway in practice) legal consequences if you sign something with fake or non-existing data, it is a false declaration.

And when you (if asked/needed by the procedure) provide a copy of your ID, you are actually giving them other data points, like your birth date, often nationality, and in some cases even the address of residence.