file name in photo

On a Mac you can show the filenames below the thumbnails as described here: How to view the titles or filenames below… - Apple Community

This will work, as long as you have not assigned a title to the photo. If a photo has a title, he title will be shown instead of the filename.

After the upgrade to Catalina you may have noticed, that the titles are gone, when viewing the library using the Photos tab. In the curated views "Days, Months, Years" your images and videos are displayed in a new, tiled view. There is no space left to show the titles or many badge overlays. The photos are cropped to the "relevant" section, so they can be laid out in tiles. But in "All Photos" you can still see the titles or the filenames below the thumbnails.

• First of all, make sure you update the system to macOS 10.15.2 at least. This update brought back the ability to see the titles below the thumbnails in the "All Photos" view. It has been broken in macOS 10.15.1.
• Second, switch from the tiled view in "All Photos" to the original aspect ratio. Then there will be some space available to display the titles. You have to click the badge to the right of the traffic light in the toolbar, to switch the aspect ratio -see the screenshots below.
• Third, enable the titles below the thumbnails in the All Photos view and the albums in the "View menu: View > Metadata > Titles. Now you will be seeing again the titles below the thumbnails in All Photos and any of the predefined albums or your own custom albums. If a photo has no custom title, the filenames will be showing instead. The filename will be slightly dimmed, and you cannot select and copy it. It is just a fake title. A custom title you assigned by typing into the title field can be selected and copied and pasted. When you sort an album by the title, Photos will ignore the filenames and only sort by the titles you assigned.

In "All Photos" try to use these settings:

• Click the tiny display icon to the right of the traffic light in the toolbar to see the thumbnails in the correct aspect ratio and not tiles as squares.
• Open the View menu, go to Metadata and enable all options to see badge overlays and titles below the thumbnails.

Here are some screenshots:

How to switch between the tiles and the correct aspect ratio to see the thumbnails without cropping:

How to enable the titles below the thumbnails in the All Photos view and the albums:

To change the title, you can either type directly into the title field below the thumbnail or open the Info for a photo with the keyboard shortcut ⌘I. In the Info panel you can edit the title, the description, or the keywords by typing into the corresponding fields.

Are you talking about a Mac, an iPhone, an iPad, or a Watch? What OS is this device running?

Are you looking at thumbnails? Or at the preview?

Generally, you can see a filename by selecting a picture and choosing Info. But Info appears differently depending on the device and OS.