It is a rare given name for a child to be named Sorrowful, but it did occasional occur. Mostly the given name of Sorrowful occurs more (but still rare) in Hyde County North Carolina. In some cases you can see, where in later generations those who had Sorrowfull as a middle name, the spelling was changed and it became Sarfull. In researching early settlers of the Eastern Shore of Virginia I encountered Sorrowful Margaret Custis (born 1681 - died about 1750), daughter of John Custis III (of Wilsonia ) and Margaret Michael. In her case, she was named Sorrowfull because her mother died giving birth to her. The Custis family has always had a certain eccentric in it, so to give a child that kind of name is no surprise.
John Custis was a well off planter and merchant who lived at Arlington Northampton county Virginia. They had at least five children of which Sorrowful Margaret was the last (makes sense if her mother died giving birth to her) . His grandson would marry Martha Danridge, who after the grandson's death, would marry George Washington. His great grand daughter would marry Robert E. Lee.
So back to Sorrowful. She married William Kendall and after his death Thomas Cable. She had as children; Littleton Kendall, Col. Custis Kendall, William Kendall IV, Ann Kendall, Peggy Kendall, Leah Kendall, Henrietta Kendall, George Mason Kendall and Ester Cable, Elizabeth Cable, and Sarah Cable. Yes she was productive. .