The data protection agency say the policy violates German laws, which allow people the right to use pseudonyms online.
The agency has demanded that Facebook let people use fake names with immediate effect.
However, Facebook said it would fight “vigorously” to keep its policy and that it has already met European data protection rules.
Thilo Weichert, Privacy Commissioner at the German data body, said: “It is unacceptable that a U.S. portal like Facebook violates German data protection law unopposed and with no prospect of an end. The aim of the orders of ULD is to finally bring about a legal clarification of who is responsible for Facebook and to what this company is bound to. Actually, this should be in the interest of the company, too.
“In so far, we hope for a fact-based debate not aimed at delaying action. In view of the fact that Facebook currently is taking the opportunity from all its members to decide themselves about their own discoverability under their name, our initiative is more urgent than ever.”