NEVER! Had that been the case how Columbia and Tristar brands still exist? Because they have the word "A Sony Pictures Company" written below. Had it been single acquisition of channels like SAB TV and Channel 8, then the case would have been different.
Even in tech world, Motorola was acquired twice. First by Google and then by Lenovo. Did they ever drop the Motorola brand? NO!
ZEE, if merged with Sony after all this dramabazi, will retain its brand but will have to write the word "a Sony Pictures Network company" below the brand. Nothing else will change.