Can the government arrest someone without releasing their name?

Immigrantion and Criminal Enforcement is the main federal agency charged with enforcing our nation's immigration laws. Well, it seems that they can arrest suspected illegal/undocumented individuals and have stated that they as an orgaization are not obligated to release the names of those arrested. Supposedly this is a policy dealing with privacy. No government should be able to arrest people and not release that information to the public.

How do we even know those who are arrested, should have been arrested in the first place? Could political protestors be arrested and not have their names released? Indeed, American citizens have been wrongly deported from the U.S. This is more common than you think.