To retrieve the element's text (as in ALL the text, subnodes included):
var value = document.getElementById('name').textContent;
Then to assigned the text to the input field in another page:
document.getElementById('myField').value = value;
Of course that doesn't work across pages. If you don't want to use server-side code for this, one simple way of doing it would be to pass the code in a query string, redirect to your form page, and retrieve the variable from the query parameters. Which sounds simpler than it actually is, as you'd need a function to add a query parameter, another one to read a query parameter, and to be sure that everything is encoded and decoded properly.
Another - bad - alternative could be to use cookies via JavaScript.
Another - better but not yet widespread - alternative could to use the WebStorage API. (see localStorage and/or sessionStorage). This will require a modern browser supporting these APIs (for instance, Google Chrome, IE9, Firefox 4, etc...)
The embedded links will provide the missing parts.