Remote desktop by IP address but not Computer Name

[John Gray]

I often Remote Desktop from home into work PCs using a VPN set up by the Microsoft Network Connection software on my home PC.
When at work I can Remote Desktop from my work PC into any of these PCs using their computer name.
When at home, for some work PCs (but not all) I have to specify their local IP address, e.g. mstsc /v:192.168.0.234 because their computer name, e.g. mstsc /v:PC34, gives an error message.

Is there anything I should do on those PCs so that I can Remote Desktop in from home using the PC name? Perhaps ipconfig /registerdns? Or by trying to connect using the FQDN, e.g. PC34.domain.co.uk rather than PC34?

I am puzzled by the inconsistency - you'd expect them all to work using computer name, or none!

Thanks!