I have seen her name written both ways.From 1850 Tippah Co., MS Census I copied it Mary Ann. From 1880 Census in Union Co., MS I copied it Mary J.I no longer subscribe to a genealogy website that allows me to look at actual census pages and am not driving any more, so I cannot go to the library to check. You might want to check the census records out and see if I might have written one them down wrong.
The only legal document I have with her signature (or a clerical copy) on it is a copy from South Carolina Archives of a deed in 1833 when David was selling some property.She signed it Mary Pannel, no initial, after being privately examined to be sure she agreed to the sale.
Since they were in Mississippi in 1840, I assume they were about to leave SC.
David left a will made out in 1883 in which he mentioned his daughter Jane Dye and the children of his youngest daughter, Amanda Cox.You could get a copy from Union Co. MS.
No I don't have a document as proof of Coggin. I heard it from an old aunt who is no longer living.
What is your connection to the family?I am descended from two of David's brothers Richard and Elias.