But if she went by Jones and was known by everyone as Jones and Jones was on her gravestone, Jones would be her CLN (unless she remarried and took that husband's name .. or she, for whatever reason, took another last name at some stage).
If I started using the last name McArnold today, and everyone from now until I died knew me as McArnold, it doesn't matter one grain of sand what anyone else thinks is my legal name; I would legally be McArnold. My government would accept that as my legal last name at death as well, even if I had never taken out any paperwork on it.
I know someone who lived with her mate for 30-some years, being known by his last name. They were not married, as he was unable to divorce his wife. The legal situation was that she was legally his last name because she was known by it, had been using it for whatever time, had not assumed its use for any nefarious purpose etc. The only possibility of a problem would be if, when he died, his children contested his Will. The way around that is to have your clever little solicitor/lawyer write it up in such a way that it was extremely clear she was meant to be the heir no matter what the marital status was. (And a smart thing would be to make sure the kids were given a decent inheritance as well, even if they have to wait 10 to 15 years to get it.) There is legal and there is legal. Marriage doesn't make a legal last name.