First, login to your Shopify Account at accounts.shopify.com/store-login. Your store name is located the URL for your Shopify account -- 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.