Hi Dinesh,
1. Do we have any possibility to change the Business Unit Name ?
There is no possibility
2. If we dont have an alternative, can we create a new Business Unit and update the users to point this one? In this process, will it impact the privileges/roles on the records the users having access to?
You can create new business units, yes it affects privileges and roles.
Thanks & Regards, MS CRM Consultant, V.Surya.