You did not say what computer or iPhone you are using or what operating systems they're running, so it's a bit hard to be specific.
So, to be clear--by titles do you mean filename? When I import pictures to Photos, they generally have filenames like DSC_1234, or something. There is also a Title field that you can see in the info window in Mac Photos, and that is generally empty. The Title field does not show on an iPhone or iPad. We usually use the word Title to be different from filename, so I'm not sure what you mean.
When looking at the thumbnails in Photos on a Mac, the Title, the stuff in the title field in the Mac's Photos Info window, appears beneath the picture. If the Title field is empty, then the filename appears, but this is not what's in the title field-- it's a temporary substitute.
Photos does not allow you to change the filename. If you want to change the filename, you need to do this outside of Photos--maybe export the pictures and re-import them after the change. On a Mac, Matti and I (and lots of others) would use Graphic Converter to batch change the filenames. But, again, this can't be done while pictures are inside Photos.
On a Mac, I use the Title Field in Photos to record the date and some detail. This shows below the Thumbnail, and you can export the pictures using the Title for the filename if you choose. The title is included in the IPTC metadata.
I use the 3rd party app Photos Workbench ($30) to add titles in batches. Photos Workbench has options like this:

I have it record the year-month-day and index number with a text description. There are many options-- you can have it include the original filename, for instance. There is also a find and replace function for titles, so I can fix my mistakes.
To send jpgs to others, I export the picture using the Title field for the filename, like this:

So one way to change filenames with Photos could be to use PhotosWorkbench to add titles, and then export with the title for the filename.