Name resolution is done through the WINS protocol (unless you configured a DNS server properly). There’s a few things you should verify
The colibri requires a unique name in the network. (Start → Settings → Control Panel → System → Device Name)
The iMX6 uses the serial number as part of the device name by default, so this is probably fine.
There must be a WINS server in the network. The Colibri learns about the WINS server from the DHCP server. Compare your PC’s WINS server setting against the one on Colibri.
Of course the WINS server as well as your PC must be reachable through your network router(s). I recommend to use Wireshark or a similar tool to analyze the network traffic.
To be sure I just verified on my desk that my PC and a Colibri iMX6 can ping each other successfully.