Why does Beowulf ask Wiglaf to build him a tomb and call it Beowulf's tower?

Beowulf wants the tall tower built at the edge of the water so that sailors can see it from a distance and remember his name. Thus Beowulf wishes to be remembered after his death. Also, as a man of the sea, he identifies with those who will come in their own journeys over the sea after his death. He wants the tower built so that "boats in the darkness / And mist, crossing the sea, will know it."

As recounted in "The Burning of Beowulf's Body," Beowulf's request is honored. The Geats build the tower "strong and tall," working on it for "ten long days." After Beowulf's monument is completed, the Geats seal his ashes within its walls and also bury the treasures won by Beowulf and Wiglaf. Once Beowulf's burial is complete, "twelve of the bravest Geats / Rode their horses around the tower, / Telling their sorrow . . . ."