In Photos there are user-accessible fields for Title, Capture Date, Caption, Keyword, and Location.

Things like filename and camera info can't be changed. Since Title appears under the Thumbnail, the title is usually short-- though it can be longer with only the first characters appearing with the Thumbnail. Caption, or sometimes Description, can be long-- I'm not sure what the limit is, but I have captions with multiline biographies of several people in a picture. In the contact sheet that I showed earlier, the first line in bold is from the Title field, and the rest is from the Caption field. For editing, it seems that Captions are hard to access, but Titles are available to scripts. For now, at least, Titles do not show in iOS, but Captions do.
For titles I have been using Photos Workbench ($30). You can do stuff like this:

Here are some choices you get:

"Counter" is an index number increasing from a start number you can choose.
My pictures almost always carry a title something like this

with a description, like Six Flags, in this case.
Photos Workbench also has a find and replace function for Titles, which I, unfortunately, make use of often-- after I've discovered my mistakes. I have used it to replace titles on several thousand pictures after I decided to change my format. Here's a name format change:

It's good that you're interested in Titles rather than Captions-- Titles are easier.