Is it a merger or complete acquisition? Incase of merger airtel might have majority stake but both brands will run independently and have separate policies. Merger will bring in benefit of reduction in expenditure involved with running of uplinking station, customer care, after sales, etc.
Though going by past trends, airtel will most probably acquire dish d2h. Also similar thing might happen with Zee. Already Zee Channels getting added fast on airtel, Zee5 content free on airtel app and many service channels previously restricted to dish d2h like Zee Theatre, Shemaroo Suspense getting added on airtel r early signs highlighting where things r heading . Lastly new channels not getting added on dish d2h is a big indicator that they r waiting for new team to take charge and make decisions as they seem fit.