Changing your name and Deed Polls

Nowadays if you want to change your name then it is probably best to use the Deed Poll system.
from http://www.deedpoll.org.uk/Overseas.html
"if you are British and reside outside the United Kingdom and wish to legally change your name, or your children's names, you can use the Deed Poll process, which has been used by hundreds of thousands of British people for over 150 years."

In old days you could just use a new name - providing no unlawful purpose like fraud was intended. Many woman left their husband and moved in with a new man and used his name. And children might use their step fathers name.Or people for some reason or other wanted a new name.

Some advice on what they did etc at
The National Archives | Getting started | Family History | Change of name

But there may not be a document - just that they did it.