In the Epic Poem Beowulf, the character Beowulf is a typical Epic Hero. This being said, as a typical Epic Hero, his name is renowned. It is through his heroic actions and epic challenges that his name precedes him.
Upon arriving at Hrothgar's lands, Beowulf's arrival is announced by Wulfgar to Hrothgar. Learning of Beowulf's arrival, Hrothgar states that he has heard of Beowulf. Hrothgar admits that he knew Beowulf when he was younger and that he also knew Beowulf's father, Ecgtheow (or Edgetho depending upon translation).
Hrothgar thanks God for sending Beowulf to rid Heorot of the monster Grendel. Given that Beowulf's name has made it to the shores of the Danes, his legendary status in known by all.