Dolly was named after Dolly Parton, because she was cloned from a mammary gland! She was cloned using the process of nuclear transfusion. Ian Wilmut and Keith Campbell headed the cloning process in Scotland.
Dolly was born in 1996 and lived for six years until a progressive lung disease took her life. She had a common form of cancer amongst sheep. While many people thought maybe her health problems derived from being a cloned sheep, the scientists in charge of her do not think that's the case.
Wilmut said they couldn't think of a more impressive pair of mammary glands than Dolly Parton, so that is why they named the cloned sheep after her.