Robert m. Proto-Germanic *hrōþiz 'fame' + Proto-Germanic *berhtaz 'bright'.
The name of two 8th C German saints, a 10th C king of West Francia, a 10th-11th C king of the Franks, an 11th C French saint, a 12th C French saint, a 12th C English saint, a 14th C king of Germany, a 14th C king of Naples, three 14th C kings of the Scots, and a 15th C king of Germany.
The Norman name arrived in England with the Conquest, but the Old English cognate was found rarely, earlier.