A New York Times article about the Presidential Medal of Freedom reports: "Mr. Obama honored President George Bush."
Because there have been two presidents named George Bush, that sentence in the New York Times isn't particularly helpful. In cases, such as this one, where it's not easily or immediately apparent from the context which president is meant, the Times would do its readers a favor by using middle initials — George W. Bush, George H.W. Bush — to distinguish.
In case you were wondering, it was George H.W. Bush who received the medal from Obama.