The default search function that is built into X-Cart 5 doesn't look into product attributes (and brand is just a product attribute in this case). Technically it is possible, but will require creating a custom module.
Also, as far as I know, this service does look into product attributes and may help you:
https://market.x-cart.com/addons/cloudsearch.html
If you have less than 100 products it will be free for you (and you can try it for free on a test X-Cart installation).