Rman not replacing logs with same name on networked drive
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 &lt;&lt;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 &lt; ${MYLOG}
fi
# add the incremental log to the permanent log
cat ${MYLOG} &gt;&gt; ${LOGPREFIX}.log
# clean up the incremental log
/bin/rm -f ${MYLOG}