How to show vendor name in addition to product/SKU i.e. "vendor - product1"

Hi together,
we have woocommerce and the matomo ecommerce-module activated - product-tracking works.

But: We have a multivendor-site and these vendors have products with the same name.

How can we add the vendor name to the product so that we can analyze the vendor/product combination in matomo?

Or: can we else filter products by vendor in an easy way in matomo?

Thanks for your help!