I use the following function:
function doGet(e) {
Logger.log( SitesApp.getActivePage().getName())
}
It always returns the name of the home page
This seems to be an issue with Google currently. All Google Sites are facing this issue. Please submit a bug report, and cross your fingers it'll be solved soon.
Here is an existent bug report of this issue. Please +1 it to give it more attention.