"To follow a brand" means to actively subscribe or show interest in updates, news, and content related to that particular brand, typically on social media platforms. Full definition
The main concept is people don't follow brands on social — they follow other people. (inc.com)
Following his brand of capitalism, he is likely to strengthen the connections between business leaders and politicians, often preferring the former over the latter. (blog.politics.ox.ac.uk)
I ordered this product as I've been following this brand for quite a while and believe in it. (shop.mfit.com)