Who has the right to bestow a professor title? (government or university)
In the United States, personal titles are almost never legally protected or regulated by the government.  This is a strong cultural tradition going back through the origin of the nation, and is in fact encoded in the US Constitution, in the "Titles of Nobility" clause:


  No title of nobility shall be granted by the United States: and no person holding any office of profit or trust under them, shall, without the consent of the Congress, accept of any present, emolument, office, or title, of any kind whatever, from any king, prince, or foreign state.


In the US, then, in general anybody can call themselves any title they feel like, including Professor, Doctor, President, and Emperor.  The title, per se, is only a matter of social convention and will be respected or disrespected based on whether other people believe a person deserves it.
The law typically only gets involved from a perspective of fraud, false advertising, public endangerment, etc. if a person uses such a title to give a false impression of your skills and certifications.  To illustrate the distinction: Dr. Dre is perfectly within his rights to use that name, but if he tried to give somebody a prescription, he could be arrested for practicing medicine without a license.

Thus, the US government does not name people professor (except incidentally, if it happens to be running the university, e.g. NWC).  Typically universities name people "professor" as a job title, but in fact, anybody can call themselves a professor or set up their own fake university to be a professor at.