By using YITH WooCommerce Ajax Search, you can add a search bar to your website, which will allow users to search via AJAX for specific content in your website, searching through posts, pages, and products.
The integration between these two plugins allows users to enter the vendor’s name and instantly get a list of their products. To do that, all you need to do is install the plugin and activate it.
Then, go to YITH > Ajax Search > Search fields. Here, you can choose to extend the search to all your vendors or enable/disable specific vendors.

Please note: after enabling brands, it is necessary to rebuild the index.
Now, if you start typing the name of a vendor, the plugin will automatically show this vendor’s products.

Moreover, when creating boost rules, you will find a new entry among the conditions that will allow you to increase the visibility of products of specific vendors.

For more details about YITH AJAX Search, please, check the official documentation.