Elias here with Shopify Support. I’d be happy to lend a hand with this!
Based on your screenshot, it looks like the “Shipping” name was used when setting up the delivery zone name in your Local delivery settings (‘Settings > Shipping & Delivery > Local delivery’). You can always change the Zone name by managing your Local delivery settings for each of your locations. Simply click Manage and edit the Zone name as shown below.
If you’re looking to change the Rate name for a shipping rate, you can do that by clicking Manage rates in your Shipping settings. From there, simply click the ‘…’ beside the rate you’d like to edit and select Edit rate. That being said, we’ve also got guides that can help with setting up your shipping zones and free shipping rates.