Is it a trunked system or conventional?
If it's a conventional system, identical radio ID's will work fine, but it will cause issues if one of the radios gets lost/stolen and the system administrator attempts to kill it.
If it's a trunked system, identical radio ID's can be an issue.
Ideally, you do want different radio ID's, but getting those ID numbers really needs to come from your employer. That means you'd need to talk to them, and let them know you have your own radio. This may or may not go over well with the management. Just be ready to justify what you have done. As an employee, you do not technically have authority to add radios to an employers system as the license belongs (likely) to your employer and they are in control of the license and responsible for whatever happens on the system, even your own private radio. Of course many agencies just don't care.