I've done something similar as pretending to be someone different to cancel a contract - I pretended to be a live dh
She said only he could cancel our sky contract (smugly or I wouldn't have done this) so I sighed and put on my gravelly voice - she said 'I know that's you!'
I said : ' I have no use what you're talking about please go through the security questions'
Which of course I knew the answer to 
I did enjoy wishing her a 'nighty night' in my normal voice at the end of the call