Is this a captive portal (CP) guest network? If so, the wireless clients will always obtain DHCP prior to authentication. Are you using on-board radius for authentication? If so, under Configuration/Services/Radius/Groups, there is an option to enter the WLAN SSID. You might want to check this setting.
Changing the WLAN SSID on an existing WLAN should not prohibit Internet access if the all the other settings have been untouched.
If under entitlement/contract, might be quicker to get a support case generated and we can review your configuration.