If you are going to present full time as your actual gender (as opposed to the legal gender assigned at birth), you will probably want to change your name and gender on as many official documents as possible. This is especially important if you will be seeking NHS surgical treatment as GICs (Gender Identity Clincs) will often use this as the start date for real life experience required before genital surgery is performed.
There are a few ways to officially change your name, and we would suggest you see the details provided in the UKtrans.info site for a fuller description (see national links). Personally I liked the statutory declaration route which is a simple document that you read out and sign in the presence of a solicitor. If you use a template such as the one below you should be charged £10 to £15 including some certified copies so you can send out to several organisations at once. The reason I liked this approach is that unlike a free deed poll there is at least some backup should an organisation query it's legitimancy.
For having the gender changed on your passport, driving licence and with some banks you will need at least a letter from your doctor such as the template attached below.
You may have heard that you need a gender recognition certificate to have gender changed on these documents , but It is only necessary to have a full gender recognition certificate for the purpose of changing your birth certificate and marrying in your gender (changing gender may also may affect pension considerations). See https://www.gov.uk/apply-gender-recognition-certificate/changing-your-gender for more details