You cannot change the name of the account holder even if the account holder agrees. You will need to obtain a PAC and port out the number to another network if you want to keep the number under your name. To get a PAC (Porting Authorisation Code) to keep your mobile number when switching providers in the UK, text PAC to 65075 from the phone you want to keep; it's free, usually arrives within a minute (or up to two hours/days depending on request method), and is valid for 30 days, letting you give it to your new network to transfer your number.
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