In order to have two SSIDs, the router's firmware has to support it. For example, D-Link DIR-825 has a "guest zone", which is essentially a separate SSID that you can use. You can choose whether you want the routing between zones enabled or not. This feature is created in order to give your house guests Internet access without letting them into your home's network, and without giving them your "main" SSID's password.
This means, getting two SSIDs is possible, but depends on firmware a specific router has, you need to research a specific model you wish to buy to know for sure.