@Ben Hizak  I’d need to see more of your setup to help with this question but technically the company should be getting assigned for a specific reason -- if Intercom is picking up the wrong company for some reason, this could mean you need to change some details in the way your Intercom snippet and data is being mapped. 

I’d be happy to look at this further with you or feel free to share more here on what’s happening and why you would want to change the company assigned by Intercom? If it’s being incorrectly assigned, rather than changing it manually I would focus on understanding why it’s being assigned to this company incorrectly because that will impact other conversations in the future.  If you’ve got one representative that’s representing multiple companies you may need to explore different data structures to better ensure conversations are assigned to the right person/company automatically.