According to The Sun, the singer believes this is how she is best known and has decided that her upcoming second album will be self-titled.
A source said: "Cheryl has decided her married name will stay. She feels the most successful period of her career has been under the name Cole.
"She's established in Europe. Going back to her maiden name Tweedy would be confusing.
It also shows she is bigger than Ashley and prepared to be grown up about a difficult time in her life.
"She is a fan of Tina Turner. Tina was divorced during her career but decided to stick with her married name because it was how she was best known."
It is also claimed that while she will keep the surname Cole in her professional life, she is still referred to as Tweedy on her passport and mail because she never changed it when she got married.