You do not have to be a British citizen to change your name by deed poll. Any adult living in England, Wales or Northern Ireland can make one, whatever their nationality, and once it is signed and witnessed it is valid evidence of your new name with UK organisations such as banks, employers, the NHS and HMRC.
People moving to the UK change their name for all sorts of reasons: to have a name British institutions handle more easily, to match the name they actually use, or for a fresh start. You do not have to give one.
A UK deed poll does not change your home-country documents
This is the important limit. A UK deed poll changes your name in UK records only. Your passport and ID documents from your country of nationality stay in your old name, and most countries will not accept a UK deed poll as grounds to change them. You would need to go through your own country's process for that, usually starting with its embassy or consulate.
That can leave your UK records in one name and your passport in another. Many people live with this without trouble, but some organisations, the Home Office in particular, may query the difference. If you want your names to match everywhere, run your home country's process alongside the deed poll.
Get your deed poll in the next few minutes
Fill in the form, check the preview, pay once. Your PDF downloads straight away — one payment of £14.99, no account and nothing that renews.
Visas, eVisas and citizenship
Changing your name does not change your immigration status, but UK Visas and Immigration (UKVI) needs to know. Your immigration status is now held as an eVisa linked to your UKVI account, and you update your personal details there. Because UKVI ties your eVisa to your passport, check with them before you change your name if your passport will stay in your old name.
If you are applying for indefinite leave to remain or British citizenship, sort out your name first or talk to UKVI, so your application is in the name you will be using. Once you are a British citizen you can get a British passport in your new name with the deed poll. See deed polls for new British citizens.