Service invoicing by foreign party

As far as Income tax is concerned, as per my understanding I don't think there is any problem if invoice is raised on any of your locations.

since it will be import of service, GST RCM may be applicable (depending upon the fact of the case), so ITC on such RCM paid will be available for Odisha plant as services are performed their. So better to take invoice in Odisha name

Also check with your bank arrangements, if they are ok with releasing the foreign exchange from Kolkata for invoice of Odisha.