After tapping on "Move to a different folder", a File Explorer screen will appear with "Move to.." in the title, starting with the root of the file system. You can tap on a folder to change the folder to where the selected file will be moved and/or renamed.

When you have navigated to the folder where the file should be put, you can tap on New in the lower right of the File Explorer. This will display a prompt where you can revise the file name before the move/rename is performed, or you can create additional folders at this time.