Well how are you going to resolve a host name? abc, do you have a wins server? if not then since its not a fqdn (dns like abc.domain.tld) you would have to broadcast for it. You can not broadcast across segments.
So no hostname across a vpn rarely work unless your bridging?
So a few options, use DNS - if your talking w2k8 server - do you have a Domain(AD) then you would have to have DNS - use that to resolve your computers name. If you setup a search suffix for your domain.tld then sure you can use just hostname portion and the dns query will auto add the domain.tld part.
Setup Wins if you want and don't have AD with DNS. Or just setup a host file on your computer that has a listing off all your machines IP and names and then you can use the names to connect like
192.168.1.100 abc
192.168.1.101 dfg
192.168.1.203 xyz
etc.
so for example I run dns on my local network at home, local.lan - and I have my computes in dns - so when I vpn in I hand off this dns
ethernet adapter ovpn:
Connection-specific DNS Suffix . : local.lan
Description . . . . . . . . . . . : TAP-Win32 Adapter V9
Physical Address. . . . . . . . . : 00-FF-79-1A-85-63
Dhcp Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IP Address. . . . . . . . . . . . : 10.0.200.6
Subnet Mask . . . . . . . . . . . : 255.255.255.252
Default Gateway . . . . . . . . . :
DHCP Server . . . . . . . . . . . : 10.0.200.5
DNS Servers . . . . . . . . . . . : 192.168.1.253
Lease Obtained. . . . . . . . . . : Tuesday, November 06, 2012 3:11:53 PM
Lease Expires . . . . . . . . . . : Wednesday, November 06, 2013 3:11:53 PM
So I can resolve hosts in my network via their fqdn, and my search suffix of local.lan
D:\>ping
i5-w7
Pinging i5-w7
.local.lan [192.168.1.100] with 32 bytes of data:
Reply from 192.168.1.100: bytes=32 time=121ms TTL=127
Reply from 192.168.1.100: bytes=32 time=121ms TTL=127
Reply from 192.168.1.100: bytes=32 time=131ms TTL=127
Reply from 192.168.1.100: bytes=32 time=119ms TTL=127
Ping statistics for 192.168.1.100:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 119ms, Maximum = 131ms, Average = 123ms