Why does Sigurd reveal himself to Fafnir?

Question

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?

Answer 1

My high-level response would be that one motivation is to display his courage in not fearing a potential curse by the Dragon.

It's an interesting point that he only reveals his identity after being called out by Fafnir, with the implication Sigurd withholds his identity out of fear.

(The reason I don't think it has to do with Sigurd wanting to be seen as truthful is the prestige conferred in many Norse sagas and myth for tricking one's opponents.)