t-online told me I needed an imprint on the website that's reachable under my domain. Seems to be some misunderstanding of German law (German commercial websites need an imprint, legally, but t-online also apply this requirement to private domains).
It is more complicated than that. There are more criteria for when you need an imprint:
(1) any kind of journalistic content on your site
(2) any kind of financial gain from showing ads or making ads
(3) organizing any kind of group of people active on German territory
(4) running a business website
There might be more, but those are the ones I remember from reading the paragraphs a while ago.
And these are, of course, vague, which means that even something like "my favorite restaurants in Berlin" could be considered an ad, or any kind of comment on politics might be considered a form of journalism.
I dislike these rules, because they basically kill German blogging scene. Not so many people want to run a blog and have every idiot on the Internet know their personal address. And few bloggers want to rent a digital office or actual office, that will send mail to them (an indirection). The German law in this respect is terrible and working against a free Internet and against freedom of voicing your opinion. It works greatly in favor for tech giants, because people resort to putting their blogging on Facebook, Instagram and other disservices. It is very anti-decentralization.
Of course, if you run a business. But then you might even have an actual physical office address for work related stuff and not have a problem giving that to random strangers on the Internet. If you are a private person simply wanting to run a blog and talk about whatever you like, then it sucks. It does not have to be your home address you are sharing, but the other options will cost you money. And no, a postbox will not be sufficient, as decided in previous court cases. It must be a "ladungsfaehige" address. There are some businesses selling services to have a virtual office, with an actual address, which then send your mail further to your actual address and notify you via e-mail and all that. Whether those are really an acceptable option when it comes to the law is a bit unclear.