First, log in to your Shopify account at accounts.shopify.com/store-login. Your store name is located in the URL — after the https:// and before .myshopify. Do not include "myshopify.com" in the name, only the phrase right before it.
For example, if your URL is:
https://universal-apples.myshopify.com/admin/settings/checkout then the store name is universal-apples.