There is a simple way of hiding the XPage name. Autolaunch an XPage using the database properties.

But there is a catch, it will only work for the first XPage so if you navigate way to another xpage the magic is gone. there is also another catch the relative path is broken so you need to add a trailing slash. Prev post about that

But that isn’t a problem when you are using XPages so If you build your main XPage and open it using auto launch options, and load the different sub pages / custom controls using partial refresh and the rendered property, the switch control or another control that can load content using a partial refresh.

Also you need to add a trailing slah at the end of the url otherwise you will get problem with dead images and resources not loading.

Your page should work as expected anyway, enjoy.