Shoutbox

There is no need for an iframe at all if you just want to popup a inputbox and then redirect the current page to your website... If you do want that the main page (where the popup is launched) to stay, then you can use Lobster's method...

So, it depends what you want.
Do you want that popup at you website which also takes the data (name)?
Do you want to be redirected to your website after the name is filled out?
Is it nessecary to use the POST method? Can't you use the GET method?
Can you be more clear about what you exactly to happen and where it should happen (in clear steps)?

for example:
(the user will not know what happens with his name after he filled it in.)
1) User opens page A
2) a popup is shown asking for his name and the data is send to page B (your website)
3) the user stays on page A

or for example:
(the user is redirected to the page which processes the name.)
1) User opens page A (your website)
2) a popup is shown asking for his name and the data is send to page B
3) that page B processes the name and outputs some data accordingly. For example: "Hi, <name>. Welcome at my website"