Braun is a common surname, originating from the German word for the color brown. The name is the 22nd most common family name in Germany. Many German emigrants to the United States also changed their name to Brown (see Brown (surname)).
In German, Braun is pronounced, roughly similar to the English word "brown." In English, it is often pronounced like "brawn," as in Carol Mosely Braun. Pronunciation is an individual choice and is hard to guess unless one is in a position to hear the person's name spoken.