There are a couple of biblical names which have such a story associated with them, and people in the 17th and 18th c. would have been familiar with the stories.
Isaac was born in extreme old age to a woman with no other children.
Samuel was born to a woman who was unable to have children for many years and prayed continually for a son.
Though I can't answer your usage questions, I can tell you that even today, devout Christian parents who have a son in one of those circumstances very often choose those names. I know several.
This message was edited 6/16/2011, 6:20 AM