If in edit view you can see a title filled in then the title is always displayed below the photo in photo view (may depend on the theme).
In thumbnail view of galleries there is an option to show or hide the title. You find this option in the customize view. Go to the thumbnail view of the gallery and open the options from the toolbar on the top (yellow background). In the section of thumbnail display there is the option to show/hide the title.
Currently there is no way to display the file name next to the image. It is displayed only in the EXIF-Info section, when it is enabled.