Yes, you will be registered as the domain owner (holder) and given all the rights for the requested domain.
Hint: To meet the legal policies and regulations of DENIC the administrative contact of the domain ( admin-c ) must be Germany-based. Publishing the holder data in the whois servers of the respective NICs is a mandatory conditon for the registration of a domain. As the domain holder you are also responsible for the violation of third party rights (e.g. trademark protection rights). So you can't own a domain and stay "incognito". A record in the responsible NIC and the respective whois server is comparable with a record in the trade register.
You can read the domain terms and conditions of DENIC here:
DENIC domain terms and conditions