He has no wife and he has no children. This a key thematic point near the end of the story. He has noone to whom he can pass his kingdom. He dies alone. He has no physical legacy - part of the reason he wants to fight the dragon himself. He wants to leave the treasure and fame as part of his legacy.
Since he has no children, Wiglaf is named king.
There are some indications that Beowulf married Queen Hygd after she becomes a widow, but it is not well fleshed out in the text. I'm not sure about kids.
I think your friend who had mistaken the character as beowulf Scylding, which apparently someone had mistaken and thought it was the abbreviation of the hero and added his name to a completely different chracter. Yes, that particular character had a father and was father to Healfdene and grandfather to Hrothgar, so it could have been a mistake.
For the hero's case, which is also called beowulf, he did not have any descendants or any children that can carry on his legacy, nobody that he can pass his kingdom, throne to, so he dies without anybody inheriting his fortune.