Do you want to know where the auth dropdown menu is defined, or where the actual Profile page is defined? Assuming you are talking about the scaffolding application, the menu is created by auth.navbar() and is included in layout.html. All of the Auth actions are handled via the user() function in the default.py controller (and the associated /views/default/user.html view).
Note, it doesn't make sense to change "Profile" to "Register" in the navbar. The way it works now is if the user is not logged in, the navbar includes a link to "Register", and if the user is logged in, the navbar instead includes a link to the "Profile" action (doesn't make sense for a logged in user to register). If you do not want to expose the "profile" action at all, you can instead add it to auth.settings.actions_disabled.
Anthony