How do I replace the image in the search results that appears near the website?

A search banner is a graphic advertisement that appears in Yandex or Google search results.  

According to Google Help, the search engine selects the image by itself:

A text result image is the most relevant image from that particular web page for the given query. Tapping it takes the user to the web page that's embedding the image. A text result image is more likely to appear for image-seeking queries.

To optimize for a text result image, follow the Image SEO best practices. Note that indexing takes considerable time, from several days to a month.