The sender is only displayed as "email@example.com" in test messages, as test messages never route through Seller Central's messaging system.
Since the test messages are just for local testing, and using your email address, it may show the name configured for that email address directly or the business name as entered at sign up. This business name may be the same or different from your actual Seller Name on Amazon (as seen on your Seller Profile).
This will not be an issue with Active messages since they are not sent directly through the test message email address.
Active messages originate from the Communications Center, route through the Seller Central Messenger Service, and are sent directly by Amazon's email system using the special email address that you see for the buyers (like this: firstname.lastname@example.org).
Amazon's system will then put your Seller name as it appears on Amazon and assign a similar, cryptic-looking, email address in the "From" address sent to the buyer.