Its just the name of the bank. eg. HSBC Bank plc.

I think that the bank can add a delay for the time it takes for them to process the cheque if you pay by cheque

Why pay £10. Write to the bank and ask them to provide you with 'details of all charges levied on my account over the past 6 years'.
Keep it simple. My experience is that they send you the statements for free because thats the only way they can provide the information you require. If they then write back and say there is a charge, send them a cheque for £10 made payable to the bank ie NatWest . Last week got £2939 for a friend on top of sums for my 2 sons. Easy peasey.

I'm about to send a letter to my bank asking for all my statements and all other aspects of DPA. I understand the fee is £10, but what I'm wondering is who do I make the payee out to? Is it just the name of the bank, or some other name? ie: the branch name itself.