Why did Abd al-Muttalib name the Prophet Muhammad?

When the Prophet, peace and blessings be upon him, was born, his grandfather Abd al-Muttalib named him "Muhammad," out of a desire for him to be praised by Allah in the heavens and by His creation on earth. It is also said that he named him thus because of a vision Abd al-Muttalib had, the interpretation of which was that a grandson would be born to him whom the people of the East and West would follow, and whom the inhabitants of the heavens and earth would praise; hence, he named him Muhammad for that reason.