Can I change the name under Apple ID where the name, phone numbers and email are listed?

Can I change the name under Apple ID where the name, phone numbers and email are listed?

I work for a company that has several iPads and iPhones that were set up with the same Apple ID, which is not a problem.

They do however all have the same person's name when you choose on the first thing under Settings that lists Apple ID, iCloud, Media & Purchases. This person has left the company and we'd like to change the name to something more generic, iPhone-MobileKit1, etc, or something.

I know where I can do it, I just don't know if there are any repercussions for doing so.

I guess the question is, can I have something other than a person's name under the Name in the Apple ID section for Name, Phone Numbers, Email.

Hope that is clear to someone because as I type it, I feel like I am not doing a grand job of explaining it. :-)

Thanks for your help!