You will need PHP or any other server-side scripting language for this.
You will need to have 3 seperate steps. Firstly, you want to gather the information, so in your flash movie, set up 2 input text fields, name and email. Then use LoadVars to send these variables to PHP. (mail via PHP and LoadVars).
In your PHP script, comprise the link to your unique flash movie by basically adding a GET variable to your link.
Then, whenever a user clicks that link, PHP will have to extract that GET variable from the link and add it to the flash movie. A good way of doing this is by using FlashVars. This is made easy with something I use all the time and is called SWF Object by Deconcept. There's a lot of examples on that page.
So, once you added that name variable from the URL to your flash movie, you can access it and output it in a dynamic textfield.