In Chapter 7 of Eyrbyggja saga we are told how Thorolf, the first gođi of Thorsness pledged his chield to Thor:
Thorolf Most-beard married in his old age, and had to wife her who is called Unn; some say that she was daughter of Thorstein the Red, but Ari the Learned, son of Thorgils, numbers her not among his children. Thorolf and Unn had a son who was called Stein; that lad Thorolf gave to Thor his friend, and called him Thorstein, and the boy was very quick of growth.
Now, apparently,the child was not sacrificed or anything, he just got a new name. My questions are:
Was this practice prevealent? We hear of extremely many ThorX-s (Thorgerd, Thorhall, Thorkell, Thorbiorn, etc...), but it is never mentioned that they would explicitly given to Thor.
Were Thorolf fatherly rights in part transferred to the god?
Did they expect any special benefits or obligations to be bestowed on the child? (Other than growing fast)