How to change the internet network from public and unknown to private and recognised?!?

i just got a new internet router which is wireless, connected it to my mums laptop by plugging it in, unplugged it, the laptop was fine, got a signal still so i connected mine just by picking up the signal and entering the internet network key, but my internet connection says its public, so it doesnt work and i cant go online, hwo do i make my laptop forget it and reconnect properly or make it work again?