With Cart discount rules you can be able to create multiple condition based discounts in the cart.
You can provide a percentage discount or price discount or Free shipping as a discount scenario.
To check more about the Cart based rules -> Click here.
Other than free shipping, cart based discounted price would be shown as a coupon name in the cart page.
You can be able to provide a common Discount name to the Cart based discount Rules.
Here is how to set it: Woo Discount Rules -> Settings -> Cart settings.
You can enter a Coupon name to your cart discount rules in the cart page.
This is how it will be displayed in the cart page: