Redhat/Fedora /etc/sysconfig/network-scripts/ifcfg-ethN files and the ifup/ifdown scripts - these use the HWADDR variable and then set the name with the ip(8) command.

Rename eth1 to eth0:

# ip link set down eth1
# ip link set eth1 name eth0

Or if like me you simply cat the ifcfg-eth1 file to ifcfg-eth0 and its still
not working after a reboot - would not take an IP address via ifconfig, this fixed it:

# ip link set down eth1
# ip link set eth1 name eth1

Given the IP/NetmaskGateway are set in the files..

Much of this article is from here - thanks!