You didn’t mention one of the most important bits. 
The numbers which are being dialed for the different business - where are they assigned?

What I believe is the most common scenario - they would go to call queues, either directly, or first through an IVR menu. 
If that’s the case for you then all you need to do is configure Call Queues > Display Settings.

Under display settings select the following:
Phone number name
Caller ID name

Then go to Phone System > Phone numbers > All numbers > click on your numbers 
and give them a name - the name of the respective company.


The result of this config
- somebody calls phone number called “Company A”
- your agents will see on their display:
Company A
Caller ID

Whoops sorry, I definitely should’ve have mentioned that! We worked with an MSP to get migrated to RingCentral so here’s how it’s currently configured. Our main office location has most of our businesses and those numbers are assigned as Auto-receptionists that feed into our Tier 1 Call Queue for the location. We have other branches that host different companies and the numbers for those locations are directly assigned under the Call Queue> Direct Numbers.

Would the auto-receptionist affect anything for your example? And would I need to revert the changes I made under each user’s incoming call info back to “Incoming Caller ID” from “Dialed Number” for this to work? 

Thanks for the response! I’m excited to test this and see how it works. 

Would the auto-receptionist affect anything for your example? 
No, now that I know your setup I think you should follow what I suggested to the T.


would I need to revert the changes I made under each user’s incoming call info back to “Incoming Caller ID” from “Dialed Number” for this to work? 
Honestly, I’ve never had it configured to “Dialed number”, so I would recommend that you revert it as it is by default - “Incoming caller ID”. I am not sure if it will mess with the display settings of the queue or if it will affect just the display settings for direct calls. There just isn’t any good reason to use “Dialed number” given that everything you want can be achieved with Call queues > Display settings.
 

Got it, well I appreciate your time. I’ll work on this today, seems like it should work great! Thank you!