How to control how page title appears in google

Hello. Any help with this would be a life saver. The problem I’m having is that I can’t seem to control my website’s page titles in Google. Since I am not good with code I use a plugin called “All in One SEO” to help with my search result titles and descriptions.

Basically I want all of my posts/articles to appear in google with JUST the page name. For example, “Graphic Design Vocabulary”. However for my home page I would like it to display as follows: “Graphic Design Services | DesignBuddyDOTcom”. It seems that whatever I set my home page title to, it automatically gets added to my post title names in google. Is there a way to prevent it from showing? Thanks