Changing your Open Graph Image
You can absolutely change what shows up when you share your website on social networks. LinkedIn, Facebook and other social media sites use "Open Graph" data to determine what information to show when you share a link, and we allow you to control this data on a per-page basis.
To edit your Open Graph data, click on the "gear" button on the top right corner of your website after logging into your account. This brings up your page's metadata for editing. Click the "Advanced SEO Options" link and scroll to the "Open Graph Image" to upload a new image to replace the existing monogram image. Please note that you will need to do this for every page in your website (and if you use your blog feature, just once for the blog "home").
However, LinkedIn does require an extra step due to their caching rules. When you first add your website to LinkedIn, they cache the image to prevent having to check your website for updates every time somebody views your profile. Unfortunately, their cache for this type of image clears only every week or two, but there is a way for you to reset it now.
First, navigate to the Edit Intro form for your LinkedIn Profile, and remove the link to your website at the bottom of that form. Then, in the address bar of your browser or in a text editor, add ?v=1 to the end of your URL, so that it reads like this:
http://[ their custom domain or Workfolio subdomain ]/?v=1
This doesn't mean anything in particular, but LinkedIn reads this "query string" at the end as a completely new URL. When you copy and paste this into the Add Link field and click Add, you should see that the Open Graph image preview changes to the expected image. You can then click "Delete Media" or click the back arrow to discard the changes, put your regular URL (http://[ their custom domain or Workfolio subdomain ]/) into the field, and click Add. You should still see the latest image displayed, and can click Apply to add it back to your profile.
I hope this helps! Unfortunately LinkedIn doesn't provide an easier way around this, so please let me know if you have any questions about the procedure above.