Aleem- you will need to add the company codes to the new Collection Segment - but you wont be able to do that - as they are linked to the original Collection Segment.
You need to go back to the business users and say that you cant change the name of the Segment (is this really a big issue - it is just a name - it wont impact the process or the solution) - and company codes cannot be in more than one Collection Segment.
It is worth challenging business requirements