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.