Hi Handy,
I've always found the direct approach works best. On the day, front up and just advise them the old name is no longer relevant or legal, these are the new details. Simple, straight forward, no fuss.
No need for any war stories on the how, when's, where's why's, it's none of their business. Just like changing your address. You don't need to tell them why you've changed your address, you just need to tell them.
Huggs
Catherine