Create (or change) a customer role to default to that CMDB role.
Assign the customer(s) to that customer role.
Roles in the Service Catalog only allow an administrator to limit the view based on Status or Category, so you cannot specifically set one particular service as available to a specific role only. To limit the view, therefore, you could create a new Status (for example, "Available-Manager") and only allow a specific role to view Service catalog requests that have the designated Status. As an example of limiting the view based on Category, you could specify that only a certain role can access services in the HR category and put a service such as "New Hires" under that category.
For example, you might:
Create a Status called "Available-Manager".
Create a role called "Available-Manager".
Set permissions so that only those with the Available-Manager role can access the service.
Add users to the Available-Manager role.
As another example, you might:
Create a Category called "HR Services".
Create, as one of the options in that category, "New Hires".
Set permissions so that only a "Hiring-Manager" can access that category.