How do the Windows machines get their names? Did you manually configure your DNS server with a bunch of
machineXX.abc.com A records (in DNS terminology, an "A" record is an Address record which maps a host name to an IPv4 address), or do they register themselves with a WINS server (perhaps one running on your local Windows 200x Server that's acting as a Windows or Active Directory domain controller)?
If you did the DNS server thing, then go to your DNS server and add an A record for your Mac.
If your name registrations and name lookups are happening via a WINS server, you can go to "System Preferences > Network > Ethernet > Advanced... > WINS" to configure your Mac to register a name with the same WINS servers that your PCs use.
If that doesn't work, then you might be using legacy Windows "NetBIOS Name Service", which is a local LAN broadcast-based name service protocol. Try going to "System Preferences > Sharing" and enabling (checking) File Sharing, then from there go to "Options..." and enable "Share files and folders using SMB (Windows)". That will launch Mac OS X's built-in version of Samba's
nmbd(8) daemons, which should allow your Mac to advertise its name via NetBIOS Name Service.