Sigurd refuses to tell his name to the dying Fafnir:
So whenas Fafnir had his death-wound, he asked "Who art thou? And who is thy father? And what thy kin, that thou wert so hardy as to bear weapons against me?"
Sigurd answered, "Unknown to men is my kin. I am called a noble beast: neither father have I nor mother, and all alone have I fared hither."
Source: Chapter 18, The Story of the Volsungs, translated by William Morris and Eirikr Magnusson
The translator notes that this is a reference to "the superstition that a dying man could throw a curse on his enemy". When Fafnir asks a second time, though, Sigurd decides to reveal himself for no apparent reason:
Said Fafnir, "Whereas thou hast neither father nor mother, of what wonder weft thou born then? But now, though thou tellest me not thy name on this my death-day, yet thou knowest verily that thou liest unto me."
He answered, "Sigurd am I called, and my father was Sigmund."
Why the sudden change of heart?