Beowulf the Boastful

I believe Beowulf is very selfish with his fame. He even says "He who can earn it should fight for the glory of his name; fame after death is the noblest of goals." (1387-1389) Beowulf's main goal is for his name to be remembered long after his deeds. He is not doing these good deeds and battles out of the good of his heart, he is just greedy for fame. For example, in the battle when Beowulf rips off Grendel's arm, when he wins, instead of helping the victims of Grendel's carnage, he makes a point of boasting his great win before anything else by raising the ravaged arm expressing his victory and seeking rewards. Meanwhile, the guards and other victims lay ed helpless on the floor. Beowulf's main motive for his deeds is fame, not good will. Therefore, Beowulf is selfish with his acts.