The brand that is shown on your product listings comes from your store name set on WooCommerce and by default is applied to all your products. This can be changed if you prefer or have different brand names for different products.
To accomplish this all you need to do is add a Brand attribute field to your products on WooCommerce.
Go to the Products menu item, then select Attributes. The attributes screen opens.

So, on the next screen add the terms to the Brand attribute. Add the Name, Slug, and Description to the Brand attribute. In this example, I have entered 'Special Brand Name' as my brand. Your brand names will be the respective brands associated with your products. Then click Add new Brand.
The Brand will be added and some additional options will appear.
One the import has completed, return to Omnivore dashboard > click on Settings > click on WooCommerce > click on Map Fields and map the new Brand field from your WooCommerce store (this is the column on the left titled Your data fields) to the Brand field on the Omnivore Map Fields (this is the column on the right titled Omnivore data fields).
If you're unsure about the field name that contains your brand data, just export all your products from WooCommerce to a .csv file then check the title of column that contains the brand data for your products. This will be the name of the field as it appears on the left hand side column on Omnivore.
Once done, return to the Omnivore dashboard once more and click on the Import from WooCommerce button to run another full sync which will also upload your products to the marketplace/s.