When you share a post on Facebook, or when Jetpack Publicize publishes a post to your Facebook page, Facebook crawls the page and looks for Open Graph meta tags in the head to build a complete post preview (with an image, title, description, …).
Jetpack automatically creates these Open Graph Meta tags for you unless you already use another Open Graph plugin, in which case we let the other plugin handle things.
You can see what Facebook sees by entering one of your posts’ URLs in Facebook Debugger:
https://developers.facebook.com/tools/debug
I can’t tell without looking at your site, but it’s most likely that the Open Graph Meta tags outputted on your site also include the site name. I’d suggest reviewing the plugin use to add those tags, and see if you can customize the output not to include the site name.
Let me know how it goes.
If you need more help, could you post your site URL here so I can have a look?
If you want it to remain private, you can also contact us via this contact form:
https://jetpack.com/contact-support/
