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Facebook Inc. was ordered by a German privacy watchdog to allow users to have accounts under pseudonyms on the social network.

Facebook may not unilaterally change such accounts to the real names of users and may not block them, Johannes Caspar, Hamburg’s data regulator, said in an e-mailed statement. The company, whose European headquarters are in Ireland, can’t argue it’s only subject to that country’s law, he said.

“Anyone who stands on our pitch also has to play our game,” said Caspar. “The arbitrary change of the user name blatantly violates” privacy rights.

Caspar and other German regulators have been fighting with Facebook for years over the implementation of European data-protection rules. The U.S. company has argued that the Irish regulator has jurisdiction over its compliance with EU privacy law.

Facebook said it was disappointed its name policy is being revisited after it won disputes over the issue.

“The use of authentic names on Facebook protects people’s privacy and safety by ensuring people know who they’re sharing and connecting with,” the company said in an e-mailed statement.

Tuesday’s order is based on a complaint by a user who’d sought to prevent her private Facebook account from being used by people wishing to contact her about business matters.

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Facebook changed the profile to her real name against her will and asked for a digital copy of her identity card or passport, said Caspar.

The Irish privacy regulator in 2011 audited Facebook and found its name policy was in line with Irish law.

The social network in 2013 was able to fend off an attack by another German regulator by convincing national courts that only the Irish authority has jurisdiction over the issue.

Caspar now argues that a ruling last year by Europe’s top court on Google Inc.’s search engine results changed the situation and allows him to regulate Facebook.

(Updates with Facebook statement in fifth paragraph.)