Bewulf's fame

I think Bewulf's quest for fame is selfish. He wants his name as high as possible and everyone to love him. That is very arognant and very selfish. Bewulf says, "He who can earn it should fight for the glory of his name; fame after death is the noblest of goals."(1387-1389) I think this shows all his fighting isn't to save people it is for fame of his name after he dies. He doesnt want to help people he just wants to look good. What does it matter if your name lives on a long time after you die as long as you know in your heart you were a good person? I think Bewulf's way of think that fame is everything is very selfish.