Sounds like you need to update your social image link preview in the home page settings:
Log in
Click on 'Website'
When you see the Pages screen, in the left panel where your linked and unlinked pages are listed, click on the cog icon of your HOME page to go into the page settings.
Then, navigate to the 'Social Image' tab and update the 'preview' link image.
That should fix it, but if not, the only other things I can think of doing is:
Clear your browser cache: Can help ensure you see the most up-to-date version of your website.
Use the Google Search Console: Allows you to request that Google re-crawl your website, which can help update the results.
Hope this helps!