You do also need an email address
You will need at least one fully functional email
address that matches your website’s domain name.

When you sign up to have your website developed, you will also need at least one fully functional email address that matches your website’s domain name. So, if your site is at https://example.com you’ll also need an email address like, info@example.com
It’s the part of the email address that follows the @ symbol that matters most, in this case.
The reason for this is that only domains with the proper permissions are authorized to send email from certain domain names. Unless you’re Google, your website doesn’t have permission to send email messages from {anything}@gmail.com. It also doesn’t have permission to send email from any domain name other than the one that you own. If the website https://example.com tries to send an @gmail.com email, the inbox that it’s arriving at will think that the message sender is trying to falsely impersonate Google, and will either send the message straight to a spam folder or block the message entirely.
Even if you own the domain name, if you host your email separately from your website, you will need to add DNS records that give your website permission to use your domain name to send email messages. This is good because it means that no one else can impersonate you and send unauthorized spam email messages using your domain name.
“But, my website is small and wasn’t made for sending email messages”
Almost all websites send some automatic email messages, for example, your website will email you if you’ve forgotten your password. Or your website may have contact forms that send email messages. It’s very likely that your website is sending email messages, even if that’s not the main objective. If you don’t create a corresponding email address then your website might not function as expected.
“But, email addresses don’t have to be able to receive messages”
It’s true that if your website is https://example.com, your website can send messages from no-reply@example.com without that email address being properly set up or actually existing. But if your site uses WordPress, some automatic messages are sent to the default administrator email address set in the settings. Also some plugins send automatic email messages to the default email admin address.
Fully-fledged email addresses also receive error responses. So if the email your website sent bounced back, you’ll be notified.
It’s best to set up at least one fully functional email address, so you can rest assured that everything will work, and if it doesn’t, at least you’ll know about it.