It is really complicated thing to do. I think best approach will be making “site title” and “site name” short single string describing your site best.
If you want to display site title or any custom string in page title then best approach will be duplicating theme that you like and editing
/user-content/themes/YOURTHEME/layout/frontend.php file and add any custom string to site title.
As we explained before we try keeping classibase as simple as possible.