If all the other pages of the site are on "abc.fullcompanyname.com" and the home page alone is on "primarydomain.com", then the home page is the only thing that can possibly be indexed under the domain "primaryname.com." (And, technically, whole domains don't get indexed; individual URLs do.) Everything else on the site will be indexed at it's own URL (i.e. on the subdomain). If you want all the pages of the site to show up under primaryname.com, you'll need to move them to that domain.
I guess I'm confused as to what the potential issue is supposed to be. The home page will get indexed at it's URL, the interior pages will get indexed at their respective URLs. Is there some issue with the home page leading you to believe there would be a problem getting it indexed?
(Noting, of course, there's a difference between a page being indexed and a page ranking well. If what you actually want to know is if the home page can get good rankings when it's on a different domain from the entire rest of the site, that's an entirely different question. The answer to which is: yes, of course -- assuming you have no technical issues, a decent inbound link profile, logical internal navigation, useful and engaging content and all the other elements that go into a well-optimized site, and you're not in an outrageously competitive environment.)