To complete your documents you need to sign your old signature above your old name, and your new signature above your new name.
You'll also need 2 witnesses who can witness you signing, they'll then need to fill in their parts. Name, signature and address.
Once you've done this for all your documents you can then contact government agencies such as The Passport Office and DVLA, and businesses such as banks, utility companies etc. Requesting them to update your name with them, they will ask for a deed poll, this is where you can send them the completed document.