Under the old navigation, a custom page was deleted by clicking the pencil icon in the main menu, then clicking the gear icon next to the page and choosing to delete. I cannot find any similar capability under Personalized Navigation. When I expand the page list under a project using the elipsis, I can add new pages with the "+" icon, but I can't figure out how to delete a page. My workaround was to turn off the new feature, go back and delete, and then turn it on again, but that wouldn't be my first choice #personalizednavigation
Once you pin the page on side bar you will get the cog wheel control. Clicking that control will give you delete page option.
And if it helps, you might check out this goofy video which shows how-to!