How do one get his her marriage certificate?

In the different parts of the United Kingdom, legally speaking, the only generally accessible way to change one's name is by usage and repute. Once you generally use a name and get to be known under this name, it will be your legal name, provided that you do not change your name for fraudulent purposes. (In theory a name change by Act of Parliament is also possible and names can be changed by royal licence, but this latter possibility is only used in cases involving nobility.)