Government Agency Domain Names...Are They Trademark or Copyrighted?

[yanhuang]

A popular website I have seen is DMVLocations.net (which is not owned by me). I was tempted to register the deleted domain name USDAFoodSafety.com because it was available, but I decided not to because the USDA is a government agency, but then so is the DMV. Are the names of these governmental agencies trademarks or copyrighted, where if we buy one a domain name with their agency name in it, they can come after us legally? Or do we have the freedom to register them because the government is "public"?

Please advise, especially if you are a domaining lawyer or have legal knowledge.

Thank you!