EDIT: RaTTus was faster
speaking at least from a Debian point of view, changing the hostname is as simple as possible:
Concerning network communication you might also want to look into /etc/hosts, where machine names are matched to IP addresses. Since you only edited the /etc/hostname file the /etc/hosts file will surely still contain wrong information.
I would consider it necessary to change the name if you want to run both Pis in one network. Of course, network traffic is based on IP addresses and your network hardware does not care about names, but as soon as name resolution comes into play you will get into trouble.