There are many different ways to measure the No. 1 bag brand in the world. One way would be to simply look at sales figures. Another way would be to look at surveys of customer satisfaction or brand recognition/awareness.
According to a 2018 report by research firm Euromonitor International, the top five bag and luggage manufacturers in the world are Samsonite, VIP Industries, VF Corporation, Richemont and Hermes. Samsonite is the clear leader in terms of sales, with over US$2 billion in revenue in 2017. However, when it comes to customer satisfaction, Hermes ranks No. 1 according to a 2019 survey by research firm Ipsos. And when it comes to brand awareness/recognition, Louis Vuitton is ranked No. 1 globally according to a 2018 study by research agency Millward Brown.
So there is no definitive answer as to which is the No 1 bag brand in the world - it depends on how you measure it!