Generally the name of a former store does not disappear until the new store moves in. Here is a look at the old Hudson’s Bay building on the Grote Marktstraat (large pedestrian street for shopping):
Hudson’s Bay is a previously Canadian, now American company which opened locations in former V&D buildings (English Wikipedia) back in 2017. Unfortunately Hudson’s Bay only lasted about two years, having closed all of their locations around the end of 2019. The stores just did not take off in the Netherlands, having lost 184 million euros in the Netherlands (article from nos.nl in Dutch). No one knows what will come next for these locations, unfortunately.
Life in the Hague 
When I grew up these stores were called “the Bay”. I still shop there as they have some good quality merchandise. Sadly, their prices are higher than the competition and they don’t get as many customers.
I haven’t been since the lockdown, but I will return when things get back to normal.