Having your network connections called eth0 and eth1 is fine if you are a machine. However, for us humans, it's nice to give them better names. For example, on my laptop, I've named my interfaces "wireless" and "cable."

To do that (assuming you have a modern kernel and assuming you are running Debian), you should edit:

/etc/udev/rules.d/z25_persistent-net.rules

Other distro's may have to look elsewhere.

After doing that - rebooting your computer will cause the new names to take effect.

However, if you don't want to reboot, you can force the driver to unbind from the interface and rebind by following the directions here: http://lwn.net/Articles/143397/.