Your customers will see this address if you email them. To have a professional look in the communication with your customers, the email address should be match your shop domain. Try to avoid to use addresses from a free mailer like ...@gmail.com, ...@outlook.com or ...@gmx.net. If your store domain is for example yourstore.com, the mail address used for customer communication should be like firstname.lastname@example.org or email@example.com.
You can edit the email address for communication with your customer in your general settings of Shopify. If you don't have a mail address with your domain, get in contact with your hosting provider or IT department.