Ny other way that we can take auto backup in oracle 11g apart from RMAN

If I correctly understand your question as: "I want to create a standby database and later on take backups on the primary like if there would be no standby present"

In this case, you do not need a recovery catalog: quote "An RMAN recovery catalog is required so that backups taken on one database server can be restored to another database server. It is not sufficient to use only the control file as the RMAN repository because the primary database will have no knowledge of backups taken on the standby database." See http://download.oracle.com/docs/cd/E11882_01/server.112/e25608/rman.htm#BAJEDHFB

If logging with RMAN, you'd have to set the filename yourself - there's no wildcard. But there is an APPEND option.

spool log to 'my_log_file' append

Similarly, invoking RMAN with the APPEND option causes it to append to any log file specified.

Our backup scripts do the log maintenance at the OS level:

export LOGPREFIX=$ORACLE_ADMIN/$ORACLE_SID/rman/log/my_backup_script
export MYLOG=${LOGPREFIX}.$$   # add the pid to the log file name
rman log=${MYLOG} append <<EOF
... various RMAN commands
EOF

#Perform error checking and notification
fgrep -i RMAN- ${MYLOG}
if [ $? -eq 0 ]
then # we had a failure - email me
   mail -s "$0 : failure for `date +%m/%d/%y`" me@myself_and_i.com < ${MYLOG}
fi
# add the incremental log to the permanent log
cat ${MYLOG} >> ${LOGPREFIX}.log
# clean up the incremental log
/bin/rm -f ${MYLOG}