President Trump is not in charge of nor responsible for the policing of States, Counties and Cities around the nation … Federal Law Enforcement is responsible for the protection of federal buildings, federal military installations and the personnel who work within them and those functions related to the sovereignty of the Country [border protection, immigration and air travel] and federal laws like Alcohol, Tobacco and Fire Arms, FBI [major crimes - like civil rights anti-trust etc]
Also, I dont believe Trump has his name on many federal buildings if any … The Federal Courthouse in Portland Oregon is named for Senator Mark Hatfield and was commissioned during the Clinton Administration - thus the plaque on the exterior of the building states “United States of America 1997 William Jefferson Clinton President”
The President should admonish those local leaders who are letting violent rioters and looters run their respective public streets creating murder, mayhem, personal and public property destruction and theft. He does have an obligation to protect federal property from illegal activities: defacement, damage and arson. He does have a duty and right to protect the federal work force from assault.
Those Mayors and Governors also have a duty to protect those same citizens and federal property from destruction and assault - instead - they are abdicating that responsibility for political reasons … they have calculated that it is better for their re-election to blame the President and federal employees rather than due their duty … its sad and actually places every federal building and employee in greater jeopardy from the loony extremes on both sides of the spectrum - who hate the government.
While currently most of the hate is directed at federal [and local law enforcement] demonizing of the federal work force will lead to harm and even possible death to federal employees ad destruction of federal facilities. It is a fact that federal institutions are always a target - this is only making it worse.