Beowulf brings the sword that Unferth gave to him, Hrunting. But the sword had no effect on Grendel's mother He defeats Grendel's mother with blessed sword made by giants that he found in her battle hall. No ordinary man could wield it except for Beowulf.
Hrunting is not the name of the sword, because Hrunting bounced off of the sea-hag. Therefore, it is not the answer. The sword that killed her has no name. They had just called it, "The sword made by a giant."