You could also check the symlinks for the device in the sysfs. The word after “drivers” below for a given network interface (eth0 below) is usually the name of the driver (cpsw below):

$ ls -l /sys/class/net/eth0/device/driver   
lrwxrwxrwx 1 root root 0 Aug  9 10:41 /sys/class/net/eth0/device/driver -> ../../../../bus/platform/drivers/cpsw

Or run lsmod and see if anything jumps out.

Either way, once you find the driver name, run modinfo to get version and other information about specific drivers.

Edit: formatting

It’s CentOS 7.x