I don't know what it is like where you live (I don't know where you live) but here we fill it out on a form. I just put that I'm transgendered and that my old name doesn't reflect my new gender.
I changed over everything pretty easily -- I had to send a photo copy of my name change certificate that came in the mail. My cell phone charged me $20, but then I found out that it is illegal for them to do that (they have to use my new legal name, and they can't charge me for it -- no one can). I was going to call, but then they reverted the $20 a week after. So, I didn't call.
The misunderstanding that a company may have is that you are changing things over to another person, but they need to be clear that you are you and they have to change the name over -- I believe the US has similar laws, but companies will try to con you our of money or the employee you're talking to doesn't know what to do in the situation and will try to do an account transfer. But, actually, if you're a woman and you get married and legally change your last name, they do not charge you for it... in this case, changing your name legally is the same thing.
I'd look into the laws of your state; you are not a new person, but your name has changed. And I'm fairly certain they are not charging every woman who gets married an extra fee when they legally change their name.