Provided we are talking about the UK, you can call yourself "Rumpelstiltskin" or "Bodgeface" if you wish. You can get a passport in even a ridiculous name if you can prove to the UK passport authorities that the name is one you have used and been known by for a period of time. I know, because a friend of mine did so, and he wasn't even British by birth.
If she has children with the same name, it will be a great deal more convenient for many purposes if she keeps the same surname. School teachers, officials, etc, will not raise eybrows.
At the time of your divorce from her you should both have signed documents declaring that in future neither would have any claims over the assets of the other. You must check that you have copies of such documents, or else you should go back to the solicitor you used at that time.