I'm not gonna link it here to not push it up in SERPs, but my blog is linked in my profile and the imprint is linked there.
One thing that "would be funny" would be having the contact information show up only for IPs from Germany
Typically it is mostly the tax office that cares about your commercial activities: if you sell stuff, they may want you to collect VAT. If you have regular income from those activities, you have to pay income tax, etc.
So my naive reading is that having ads is fine, because you are not actually selling something. Having professional information and getting paid is also fine. Having a hobby and occasionally selling something as part of your hobby is fine.
The word has been chosen specifically and distinctly in this field of law so it can mean something specific, not the run-of-the-mill meaning of „commercial“.
You show ads (or Wordpress does for you in the free offering)? Geschäftsmäßig. For certain.
You have a web site with information that is interesting to many people (maybe how to repair bikes)? Geschäftsmäßig. Very probably.
You have a photo gallery of aunt Mary‘s 80th birthday. It‘s password protected, and you share the password only with family. Everyone else only sees the link text „Aunt Mary‘s birthday“ and noth8ng more? Not geschäftsmäßig. For certain.
Everything between examples two and three? Uncertain. Assuming „geschäftsmäßig“ is a good idea.
Privacy in Germany seems to be complicated, in one way some things are much more private, but you can't have a website without a mailing address.
It gets interesting when you‘re in any way, shape or form having a business (even a non-profit or a club — anything that is not personal). Suddenly there are other organizations that can be seen as competitors (another freelance designer, another sports club in town etc.).
And now you‘re not being fined by the state, you‘re being sued by other private parties. Because that‘s unfair business practices. You‘re not following the law, so you have an illicit advantage.
Also sitting hacker jeopardy champion, huh? Nice :)
That being said: No, you cannot just hide the address in an image - that would be illegal (the imprint information needs to be "easily parseable").
This person sometimes gets called ironically „Sitzredakteur“. „Sitting editor“. Not because he is currently the editor, as in „sitting president“, but because he‘s the one who is going to sit in prison.
Such a service enters a contract with the domain owner to forward (or scan and mail, or shred, or whatever) everything (or only non-spam) that is sent there.
The law is happy, because that is your address now, and failure to forward is something between you and the service you used; you bear all responsibility wrt the sender.
The author of a popular novel writing application offers that for his customers, as many write under a pen name and don‘t want their name to be publically known.
Other than that... nothing. You could employ a lawyer, but that would be expensive. You could get one of those „hire a post box“ services, but again, too expensive if not really used for business.
Some registrars offer that, but not for .de domains.
They're not too expensive, at least in the US. I an extra-small size PO box, and it costs the equivalent of $7 a month if rented yearly. Besides domain registrations, I've also used it as my mail forwarding address when moving, to help shake off junk-mail senders.
The GDPR is about informed consent. Do you want a domain? Yes. Great, now we need your name, and we'll put it into the WHOIS. Do you consent? Yes. Great, here's your domain. No! Okay, then you might try a different TLD, that doesn't require WHOIS publication.
The part that the GDPR is very much up to the courts, is that whether WHOIS publication is necessary for the function of the domain. Because if not, then it can be argued that it's an undue burden and it should be a separate thing, so the lack of consent for it must not mean domain registration rejection. However, ICANN thinks differently about the issue.
It is not (e.g. see the paid privacy guard services), and the article 29 working party (WP29) has been telling them this since 2003. ICANN has been ignoring it for 15 years. Until now, there was no way to enforce that. And now they reap what they sowed, with registrars stuck in the middle.