For me that would depend on the context and brand power or product type. In the industry I am currently working for this does not matter too much yet as I assume with IT and online / mobile apps it will become more important. Passengers are captive in the airport (once passed security they need to wait there for their planes) and the name of the stores where they do stop to shop do not really weight much in the balance for common goods, the main difference is mainly in luxury goods but in this case anyway as per contract with the landlord / airport authority during the bidding process we often have to bring with us to operate the luxury stores some partner brands. Thus in fact in the history of the company I currently work for the brands of the acquired company were often kept. And for other industries if the target has a very good portfolio of brands or a well know name I would be very careful in the management of brand / name change. such a transition could be risky and push some customers away.
It depends on the target and industry. Marketing DD is important to understand the target’s brand value and work out a branding strategy: If need keep the brand; if not, how long to keep it and how to migrate the branding; if yes, what would be the marketing position and how to avoid the competition with your own brand.