I changed my name a few years ago.
The UK has two ways to do it :
1. Common law - you just tell everyone to call you by your new name. Some companies will be happy to bill you in your new name, others need legal proof as below.
2. Deed Poll. You go to a solicitors and get a legal document drawn up, for about £50, certifying your change of name. No reason is needed. You can then show that to the banks etc to get your credit cards, passport etc in your new name.
As mentioned above, the key thing is that there must be no attempt to hide your identity or evade anything.
Some people deed poll their names to strange things, like Mr IhateMcDonalds, often when in the middle of a court case against the entity they don't like.
RandomStory: My favourite non-entertainment-related namechange is Henry Morton Stanley, the famous American explorer who discovered Dr Livingstone in the jungle with the immortal phrase "Dr Livingstone, I presume?"
He was actually born with the name John Rowlands to a grindingly poor family in a Welsh coal valley - his parents weren't married, his father died soon after, and his mother refused to look after him, so as an illegitimite, he grew up in the harsh workhouse.
Escaping to the USA at 15, he encountered a wealthy trader in New Orleans, named Stanley, whos name he assumed, reinventing himself.
All his life, he was obsessed with fear that people would discover his real working class origins, his illegitimacy, and that he wasn't really called Stanley. As an old man, he wandered the graveyards of New Orleans, looking for graves with the name 'Stanley' that he could claim were ancestors of his.