It is possible for the registration or use of a domain to infringe the rights of others. DENIC makes it quite clear in its Domain Guidelines and Domain Terms and Conditions that it is your duty, before you register a domain to check whether this domain might involve infringing rights. Apart from that, of course, it is in your own interest, to perform such a check, since if, in the final analysis it transpires that your domain does infringe the rights of others, you will, in case of doubt, find you have problems with the holders of those rights, resulting in the loss of the domain.
In order to find out if other people might have conflicting rights, the least you can do, for instance, is the following:
Firstly, you should see if there are any (trade)marks that are identical or similar to your domain that have been registered or applied for with the German Patent and Trademark Office (Deutschen Patent- und Markenamt , DPMA). You can find that out from the information centre of the patent office, through a commercial (trade)mark search service or with the assistance of patent attorneys or lawyers.
Secondly, you should check whether companies that are identical or similar to your domain have been entered in the commercial register. This sort of search is already available online (at least partially). Apart from that, you might find that a German Chamber of Industry and Commerce (Industrie- und Handelskammer, IHK) would be able to assist you or, again, you could turn to a legal professional.
Thirdly, it is advisable to make use of the other search facilities available, such as Internet search engines, commercial registers or even the Yellow Pages.
If you find out that someone else might also have a right to the domain, you must also do what a court of law would do in the event of litigation, namely, weigh up whose right is greater, yours or the other party's. This is exceedingly difficult to do, since even court judgements in domain cases are partly contradictory. Reviewing these judgements, one aspect that usually seems to play an important role is "priority", which means establishing who has been effectively using a particular designation longer. Another important consideration is the public familiarity with the designations and/or their users.
If there is any doubt (especially if you yourself feel apprehensive), you should most certainly obtain professional advice (from a lawyer, for instance). In unclear cases, paying for specialist advice beforehand often costs a lot less than being sued later on by someone whose rights you had overlooked. You might also find it helpful to search for further information yourself (perhaps using the Internet) on matters such as court judgements.