The MT cookie is named "user", and it should be from the host where you run MT. As for why it wouldn't be deleted... it's hard to say. Is it possible that the host in your CGIPath doesn't match up with the host that you use to access mt.cgi? Even if it's www.foo.com vs foo.com, that could cause this issue (potentially).

For some reason on my machine at work, it won't let me log out of my MT implementation.  It brings up the logout screen, but then whether I enter information or not in the login/pw fields, it still logs me in as my user name.

I tried deleting any cookie that looked related at all...