You can move a published page to a different category by using the 'Move' menu available on any page or page list view:
This will bring up the following menu allowing you to choose a different category and folder to move this page into.
You can also update a page category when editing a page. From within the edit view for a page use the button on the top left to choose a new category for the page (you can also create a new category from this view):
Bulk moving pages
You can bulk move any number of items from one category or folder to another. All moving happens from the category view, (not from within the folder view).
Once you’re inside a category, click on the checkbox on the right, above the contents of the category. Select folders and pages that you'd like to move by using the checkboxes to the left of each page and folder.
If you’ve selected just pages, you can choose the category and the folder in which they belong. If you select folders, you may only select a new category (we don’t support nested folders at this time).