"The voice called after him, "O Muhammad, you are the messenger of God, and I am the angel Gabriel."
Allah said: "Muhammad is not the father of [any] one of your men, but [he is] the Messenger of Allah and last of the prophets. And ever is Allah, of all things, Knowing." Quran 33.40 (Surat Al-'Ahzab)
Muhammad did not have to say anything.
And here's
Joseph Smith's version of the same kind of thing happening to him...
Three years after
Joseph Smith’s First Vision, God sent the angel Moroni to instruct Joseph about restoring the gospel of
Jesus Christ.
While I was thus in the act of calling upon God, I discovered a light appearing in my room, which continued to increase until the room was lighter than at noonday, when immediately a personage appeared at my bedside, standing in the air, for his feet did not touch the floor.
He had on a loose robe of most exquisite whiteness. It was a whiteness beyond anything earthly I had ever seen; nor do I believe that any earthly thing could be made to appear so exceedingly white and brilliant. His hands were naked, and his arms also, a little above the wrist; so, also, were his feet naked, as were his legs, a little above the ankles. His head and neck were also bare. I could discover that he had no other clothing on but this robe, as it was open, so that I could see into his bosom.
Not only was his robe exceedingly white, but his whole person was glorious beyond description, and his countenance truly like lightning. The room was exceedingly light, but not so very bright as immediately around his person. When I first looked upon him, I was afraid; but the fear soon left me.
He called me by name, and said unto me that he was a messenger sent from the presence of God to me, and that his name was Moroni; that God had a work for me to do; and that my name should be had for good and evil among all nations, kindreds, and tongues, or that it should be both good and evil spoken of among all people.
And people choose to believe some of these and reject others. And some people reject all of them.