I know from when I worked in call centres this was done a few times. Not that I'm condoning it but the call centre staff have to effectively believe what your telling them. If you're a guy claiming to be a woman or vice versa then the staff have to go with it as long as you can clear other security. These days with all the gender neutral and discussion on trans rights and so on I doubt anyone would dare question you for fear of bringing a discrimination claim of that nature on.
Of course the legalities are a little more gray-if contract changes were made by someone who could pass security but had lied about their identity which caused disputes, the person themselves could be liable for any action taken, though proving it would be difficult. I suppose ultimately it would come down to the fact that the actual account holder must have provided other security details to the pretender so they'd have brought it on themselves and would have to face the consequences.
If I've read up properly mind when the new billing system comes in pnet are bringing in a nominee system so an account holder can authorise someone else to deal specifically with billing, and relating it to this thread I'd assume that would cover changing direct debits. Doubt that extends to contract changing but it does at least give more flexibility.