Multi-tenanting?

Hi, Can some help?

I have several departments and companies. I would like the company a/o the department name within the company that is being called to show when an extension is called. This would be based on either the DID called or the extension selected through the auto attendant.

i.e. : Sale – company A or Sales – Company B or Management – Company A or French – Sales – Company A

I would also like to be able to select from that list so that the caller ID received by person called on outbound calls is the company / department desired by caller. Same / similar examples as above.

Are both called multi-tenanting or is one called one thing and the other something else?

I am reasonably familiar with extension naming on my phones, the flexibility of auto attendant, DID and inbound routing. So I know that I can do parts of this on a static basis but I have not figured out how to do this dynamically or how to do this for more names than I can list on my screen/soft keys. By the way, I have Astraa 480i sip phones.

I understand that I can create prefixes i.e. 9 or 8 etc to select outbound trunk but that approach has its limits.

I understand how to link an extension to an inbound route but if I want the line showing on all phones in office, the only way I have figured out how to do that is by way of extension and then I cannot control which phone gets an incoming call to that extension number.

Could someone advise how I explain above in Telephone speak and then any suggestion of how to accomplish this would be appreciated.

Thanks

Regards

Peter