To ping the computer name you need to have the fully qualified domain name address, that is resolvable back through the DNS.
e.g. computername.subdomain.domain.com
It is very rare that internal systems will expose or be resolvable across the internet / intranet boundaries. They would have to be explicitly set up to achieve this.
Typically the gateway would be the last point that would respond.
You ping a name the same way as you would an address as can be seen in this example:
http://compnetworking.about.com/od/workingwithipaddresses/ss/how-to-ping-the-ip-address-of-a-computer_3.htm[
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See the VB.net documentation:
http://msdn.microsoft.com/en-us/library/he5sca5t(v=vs.90).aspx[
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