When she launched Crazy Stupid Love in June 2014, Cole was still her legal name which she had kept after divorcing Ashley. That's why she was able to use it at that point (although to me it seemed to be a bit of a weird choice to revert back to her ex-husband's name, after being "Cheryl" in 2012).
She married Fernandez-Versini in July 2014 (incidentally in the same month she released the single), so it was at this point that she lost Cole as a name. For the releases of I Don't Care and Only Human, she went back to "Cheryl".
Obviously since then she divorced, and her name is Cheryl Tweedy (maiden name). Evidently she's decided to stick with simply "Cheryl" for Love Made Me Do It, which I'd say is sensible. Anyway, there's no logic to her ever releasing as Cheryl Cole again.