You need to have the ServerName directive inside the VirtualHost configuration i.e.:
<VirtualHost *:80>
ServerName www.example2.tv
ServerAdmin admin@example2.tv
DocumentRoot /server/sites/tv/public
<Directory /server/sites/tv/public>
# This relaxes Apache security settings.
AllowOverride all
# MultiViews must be turned off.
Options -MultiViews
</Directory>
</VirtualHost>
You can examine your configured VirtualHosts using apachectl -S - this will print a list of all the configured VirtualHosts and their corresponding config files