Internet Access Name

Can someone please tell me what is the name usually on Internet access? It seems to be no name but that's because I removed it to protect the identity. I know that it is usually the Domain name but if it is part of a WorkGroup then what is it? I don't think it's the WorkGroup name because it is written differently in My Computer as the default 'WorkGroup' name.

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It should say "network" above internet access if using ethernet cable or the actual SSID if using wireless.
 
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