I understand in Unix Oracle-Solaris OS the zoneadm list command will easily show all the available zones.But if I am logged into a non global zone there is no easy way to get information about the global zone.I see the arp command can be of some help because it will return the NIC mac address. Then with the NIC mac address I can arp again to get all the machine name associated with that (NIC) mac address.  This process sounds kind of intricate to me.Is there any better way to get that info? 
Find out global zone Name once you logged into a NON global zone
solaris;opensolaris;solaris zones
There is no supported way and this is by design. Non global zones are isolated. The arp trick isn't always reliable and won't work anyway with exclusive IP zones. Should you want to have this information available, you can implement your own method, for example writing a file like /etc/globalzone as of course the global zone can access every zone file system. 