You can change your store name in Settings>General
You can change your domain or buy a new one in the domain sections.
I know it's difficult for new members to take any change in Shopify. To change your store name, you can follow these steps on this instruction.
To change domain, you need to buy a new domain name and set it as your primary domain, here is instructional writing on setting primary domain.
Hope it help!
Changing your domain doesn't simply changing your store name, you need to buy a new domain, either from Shopify or from a third party.
If you want to buy a domain from Shopify, here's the instructional article from Shopify: https://help.shopify.com/en/manual/domains/add-a-domain/buying-domains
If you buy a domain from a third party and want to associate it with your existing Shopify store, then after buying the new domain, you have 2 options:
Hope this helps.