I have a form and I am using Javascript to validate the form so if you leave a field blank it will alert "Please fill in your Name".
If I go to the link directly, it works perfectly. But this is kind of like a Widget so I am using an iFrame to embed it into other sites. When I embed it, and click Submit with an empty field it says: The page at http://www.example.com says: Please fill in your name
Is there a way to get rid of that?
No, there isn't. It is an anti-phishing feature.
If you want a dialog without it, then you have to fake it using HTML elements in your page.