Let's assume I'm a minor, e.g. 16.
But I earn around 3000 euro a month through online business (e.g. Fiverr, YouTube or Twitch).
However, I did not show my name, age or face on the respective platform.
How can the state then know that I'm making money and that I should therefore pay taxes?
(this question is of course just pure curiosity lol)
The state knows nothing about it. Those who pay you money must certainly state that.
Oh right
Those who make money will report it.
Exactly, they have a bookkeeping obligation and note all contacts in order to be able to prove where and how much money has flowed into possible checks by the tax office. And on this basis, the FA then asks you where you stated your income.
But you gave them your e-mail address and your bank details, otherwise you won't get any money, your name and bank details are proof. This is used to access your ID number. The bank has your ID number, without which you will not get an account and so it will be reported to your responsible tax office (the bank is obliged to provide information, you have signed that when creating the account. If you do not register it, it goes in the direction of tax fraud and they understand State little fun. The solution would be to cycle to YouToube by bike, give the wrong name and take cash with you. That would then be illegal work and would also result in tax fraud.