No, if you marry and become Jones then it is Jones, nee Smith
Sometimes the word "nee" in between two surnames. ie. Abigail Jones nee Brown. This indicates that although her name is Jones now, she was born Abigail Brown.
Nee is your maiden name. You may see in writing Jane Doe nee Smith. That would mean Jane Smith married John Doe and now her name is Jane Doe. It's actually the feminized past participle for naitre which means 'to be born'.
I would say the most formal and consistent way is to use nee, as in Mary Jones (nee Smith). I wouldn't use a hyphen because that looks like she hyphenated it after marriage.
Irish actor Pierce Brosnan was born to carpenter Thomas Brosnan and May (nee Smith).
Johnny Nee was born in 1890.
Danny Nee was born in 1945.
Patrick Nee was born in 1943.
Chong Nee was born in 1975.
Kevin Nee was born on August 21, 1985.
Tan Hiok Nee was born in 1827.
Watchman Nee was born on 1903-11-04.
Yeoh Ken Nee was born in 1983.