Connecting locally and remotely work a little differently.
To connect locally your machine can look up its own hostname in the /etc/hosts file. On most Linux systems, if you use the system setup tools to change the hostname (like yast on opensuse, or setup on centos), it also changes the /etc/hosts entry for you. If you changed the hostname manually, though (for example by editing /etc/sysconfig/network on centos), the /etc/hosts file would not be updated as well. You can fix this by editing the /etc/hosts file and adding an appropriate entry, like this:
127.0.0.1 localhost.localdomain localhost mycentos
Once you have done this, "ssh mycentos" should work from the local machine.
For connentions from another computer on the same network, the other computer also needs a way to translate the name (mycentos) to its IP address (192.168.1.70). If you are running a Domain Name Server (DNS), the best thing to do is to add an entry for this host to the DNS. If not, you will have to add this entry to the hosts file of the other computer.