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:

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