You have the ability to point your siteground domain to your Shopify store so that customers can enter the third-party URL into the web browser and visit your online store. This requires going into your domain providers admin panel and changing the CNAME and A records to point to Shopify’s credentials. That’s all that is required.
An auth-code that you mention sounds like a step that would be required if you were to transfer your domain away from your provider (Siteground) and transfer it into Shopify which is a different procedure altogether.
If you are simply looking to point your hosted domain to Shopify, you can follow our step-by-step guide here that will show you how.
If there is anything else I can help you with, please let me know.