I am trying to use FaceBook Registration Plugin (http://developers.facebook.com/docs/plugins/registration/). It already has name field which I dont want to use instead i want to use my own First Name and Last Name fields Is there a way to do so ?
In the iframe url of the registration plugin, you pass in a json object listing the fields you would like on the form.
You can specify named fields (ie ones that exist within Facebook and so can be pre-populated) and also custom fields (anything that facebook doesn't know, but you might want). For example:
It's worth noting that facebook already has named fields for firstname and lastname - you can ask for these and facebook will pre-populate the fields, but allow the user to change them.
All this is documented at https://developers.facebook.com/docs/plugins/registration/
If a user is registering to your site using the plugin, they are trying to connect via Facebook and therefore would like to have their information auto-filled. If they do not, then that Name field can work for a First Name and Last Name by allowing them to enter their full name.
The problem is, that plugin is optimized for use by Facebook users AND non-facebook users, shown here:
With that said, they intend for this form to work for non-Facebook signups as well. I don't believe you can edit the forms since it uses an iframe and calls those fields through it with no user-allowed editing of the plugin. However, this doesn't mean that you could use the Facebook API to create your own plugin, or maybe a CMS you would use would have its own as well...
Another option is to have your own form, but have a "Sign In with Facebook!" link.
To answer your question directly: No, it does not look like it is editable in any way, but there are alternatives if you do not appreciate the way that the form already works.