No, your domain name won't be taken away. But the copyright holders (creators/authors of the content) can send a DMCA or copyright complaint to your webhost and they will suspend your hosting.
You can avoid this issue by hosting in DMCA-ignore servers, or offshore servers that is outside U.S. jurisdiction.
As for domain name, it can be taken away if it contains some trademark term, or when the previous owner of the domain name accuses you for using it with intent of 'bad faith' (there's 3 criteria that needs to be fulfilled). In this case, they can file a UDRP with WIPO and ICANN. If you fail to respond or lose the case, the domain name will be transferred to the trademark owner or previous owner of the domain name. In rare circumstances (and a foolish decision), the trademark owner or previous owner of the domain name can opt for the domain name to be deleted and void of ownership. Of course, this would be a dumb move as anyone can register the domain name again.
There are rare cases where your domain name can be seized. But that's for serious cases (e.g: FBI and government agencies shutting down the website and displaying that dreadful image). Again, that's if you commit some real serious deal. And getting this is like striking the lottery. Only worry about this when your website gets too big and everyone's talking about it
In summary: having lots of copyrighted content won't make you lose your domain, but your webhost provider can suspend your hosting.