December 3rd, 2015
There's a protocol called Open Graph that allows you to specify metadata for social media sites. Add some these tags to your <head>:
<meta name="og:image" content="path/to/image" /> <meta name="og:site_name" content="Site Name" />
Now when you link to this page on a social media site, you'll get the preview you want. Provided of course that the social media site reads the Open Graph metadata.
Check out more options on the Open Graph Protocol site.