Can the name of the photographer be added during upload of photos?

The current admin user uploading is actually set as the "owner" (same on album creation). Is that what you mean?

I mean that everybody can see, when looking at a photo, who was uploading! ID of uploader ...

If you mean on the site itself you have to edit the theme to display it. On the theme's image.php you can use echo $_zp_current_image->getOwner() to printout the owner id name.
https://docs.zenphoto.org/source-class-Image.html#1228-1237

For other display like the full name you have to additionally use the Adminstrator class.
https://docs.zenphoto.org/class-Zenphoto_Administrator.html

Thanks !! It works fine