Yes, you can change your name after divorce or the end of your civil partnership. Your surname does not change automatically upon the granting of your Final Order of Divorce (or Decree Absolute). You will remain known by your married name unless you decide to take steps to change it.
For those who wish to revert to their original name, you may be able to simply show record holders (such as the Passport Office / DVLA / HMRC etc) your marriage/ civil partnership certificate and a copy of your Final Order or Decree Absolute. Some organisations will accept these documents as sufficient, but others may not. Some may require a more formal document.
For this reason, many opt to change their name formally by Deed Poll. This is a legal document confirming your name change. You can apply online with the High Court to put your name change on public record and pay a fee. It can take several weeks to process, but once approved, you will receive a sealed Deed, and can then provide this to various organisations as proof of your name change.