@Anonymous Whilst you can do that you don't need to you can just change the domain name of your existing store if you want.
Here's the details on domain name set up for Shopify
If you don't want to go that route and want to physically move the products you have created from one store to another the you can just export them as a csv file and then upload them to your new store. But I would have thought changing your domain name for your existing store is a better route.
You have stated your problem very precisely. I am dropping a link here which might help you, check it once.
Hope it's beneficial..!
@Anonymous yes that's correct your can't change your myshopify domain e.g. name1.myshopify.com to name2.myshopify.com but you can change name1.com to name2.com by buying a new domain and using that as your primary domain.
If you have only just started your store and you want to change your myshopify domain address then you might be best to close your account and start again but before you do that it would be worth contacting Shopify directly to see if they can change it for you.