Ana here, from the Shopify support team. :)
To answer your question, yes - you can change the name of your store. You can do this in Settings>General:
However, one thing that you won't be able to change is your Shopify username, the .myshopify.com URL that you use to login. If you added a custom domain to your store though (in Online Store>Domains) and selected your custom domain as your primary domain, that original .myshopify.com URL is never customer-facing and you would be the only one who sees this.
If it's important to you that this matches to your actual store name, you will need to create a new account. If you'd like to do this, here's some information on duplicating your store so that you can create a new account without losing what you've done so far.
Hope this helps! :)