I would suggest Dolly's name was Rachel after her mother! My Harwood lineage from MA to VT to NY to WI used nicknames or middle names when named for a parent or grandparent. In fact I am a grand daughter of a Mary and was never known as Mary. I was nicknamed, Dolly Harwood and still have uncles and aunts who call me Dolly at the age of 63, born in 1953. The name Nancy Lavina Harwood was called Viney, Nancy Anna Harwood was Anna. Irene was Rena Harwood, Aurelia is on census records as Rella. The males were most often treated middle names, Helon Noel was Noel Harwood. Check Holland NY for Harwoods in the cemeteries too, if a Rachel child is buried before Your Dolly was born she could have been given the same name as a deceased sibling and then nicknamed. A terrible epidemic of yellow fever swept through the NY River valley, Great Lakes and St Lawrence in the 1820's and 1830"s. Because of Dolly Madison's heroic acts of saving White House historic artifacts Dolly became an extremely popular nickname.