I can't edit the top link bar items on the SharePoint 2010 site. The option is simply not there in Site Settings.

Question:

Maybe some feature I need to activate?
Also, is there a way to remove the site name placed on the top link bar?

Answer:

This option is hidden when SharePoint Publishing Infrastructure site collection feature is activated on the site (activated by default in lms sites). 

But there's an option to go to this link directly. You need to add /_layouts/topnav.aspx to the site URL to get there. 

It won't be possible to remove the site name from the top link bar until the mentioned feature is activated - it places this link by default on activation with no option to delete it.