Getting TNS Name from connection string
The instance's TNS name would be defined in the tnsnames.ora file on your system. When you bust that file open, you'll see something like...

MyOracleInstanceTNSName =
 (DESCRIPTION = 
   (ADDRESS_LIST =
     (ADDRESS = (PROTOCOL = TCP)(HOST = 192.168.1.0)(PORT = 1521))
   )
 (CONNECT_DATA =
   (SERVICE_NAME = ORA12)
 )
)


The instance name (defined in the file) is really arbitrary; meaning, you can name it whatever you want. So, in the example above, I named it MyOracleInstanceTNSName, but I could've named it something else.

In the professional world, we typically use the same name across hosts, but that's a convention. This way as we share scripts or talk about instances, we're using the same name. That's a while lot easier than remembering that Bob's "foobar" instance is the same as your "bigSexy" instance.

You can find this file in ${ORACLE_HOME}/network/admin on most systems. You should be able to find (or define) the tnsname for the instance you're using there.