I\'m writing a web application that\'s supposed to be embedded in other people\'s websites (kind of a widget). I\'m using Google Analytics to track all the people that visit
Don't have to use different cookie names as Google Analytics happily works with multiple trackers on the same page. See answers for question Google Analytics - Multiple Trackers for Several Accounts?.
Update
It turns out that using multiple trackers is a working method but has some pitfalls. One of those, that is, you cannot apply different user segmentation for each of them. John Henson demonstrates a workaround that coerces GA to use different cookies, may be you should check it.