YITH WooCommerce Bulk Product Editing is the plugin that allows you to edit quickly one or more details for an unlimited number of products at the same time.
The integration between these two plugins allows you to assign the same brand to multiple products at the same time.
After installing and activating both plugins, Brands will be included in the Enabled Columns allowing you to assign your brands with a bulk action.
For further details about YITH WooCommerce Bulk Product Editing settings, please refer to the official documentation.