Need Images in Galleries to show up in Google Searches

I need some serious help, so please respond ASAP.

My client has been hounding me on this issue. He really needs the images I set up in the galleries on his site to show up in image searches. I have added name, artist and site name in the Tag spaces, but the images only show up at best when I go into Google search and add the site name, Gallery East, in the search terms. He needs them all to show up by name or title alone.

Do I need to be more specific in the alt and Tag spaces? How do I do this? Please be as specific and step-by-step as you can.

Site is: https://galleryeastnetwork.com/wordpress

https://www.ads-software.com/plugins/nextgen-gallery/