Can I use Amazon's SES to send a display name with the source email address?

With the Java SDK you can include the display name in the sender field using the format:

John Doe <john.doe@example.com>

I assume it is the same with the .NET SDK.

Just use the .ToString() method from the MailAddress object, and you'll get the John Doe <john.doe@example.com> string. Send this string to AWS.