Would the name of the restaurant be referring to Mrs. Ashley Wilkes?
Just like there was a real Mary Mac (Mary McKinsey) who started Mary Mac's Tea Room -- the Atlanta equivalent to Mrs. Wilkes's. It was taken over in the 50s by Margaret Lupo, who ran it until her retirement in the 90s. It's still around, but it's run by a young fellow now - he's done his best to keep the food the same.