Can my Skype phone have a different number than my Skype internet?

I have a Skype account and I recently bought a Skype phone so my daughter could have some privacy talking on it in her room. Is it possible to give that phone a different number just for that phone and still keep the number I have for my Skype internet? Right now they seem connected, for instance if I change my password on the phone, it affects my internet account. I know that you can buy additional phone numbers, but I didnt know if it would fix the problem. Thanks for all who answer!