If you see this that means the RPi rebooted once and OMV's so called motd got displayed (this is not important for you but for other people reading here). Which OS are you using normally? Windows? If so please open cmd.exe, try ping raspberrypi and post the results.
The OMV Image for RPi needs Internet access on first boot to finish the installation otherwise you won't be able to access. Your symptoms indicate name resolution problems (DNS).
Is there a chance that the image (on the OMV site) for the RPi is faulty?
Nope. But there is a chance that your download got corrupted though unlikely given that the install boots flawlessly and even rebooted. But it seems the RPi has no Internet access and as such OMV won't run.