Greetings,
Since I see a few questions, allow me to clarify a few things:
Users do not need to fill out the name change request form to receive the phial of Fantasia.
The name change form is entirely separate from the character appearance change, so please do not fill out the name change form. I've edited the original article to help make this even more apparent.
Also, I see some users saying they have not received a phial of Fantasia on their version 1.0 character yet. Have you logged out and back in since you started playing? You'll need to do that for the mail to arrive in the Moogle Delivery Service.