On Linux (and probably other unices), there is a file called /etc/syslog.conf which governs where your output will go. You can add a line like

local2.*  /var/log/your_log_name
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This defines the local2 category for your use.

Include Sys::Syslog in your script or module:

use Sys::Syslog qw(:DEFAULT setlogsock);
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Then make a sub like this one:

sub syslog_event {
    my ( $type, $message ) = @_;

    Sys::Syslog::setlogsock( 'unix' );
    openlog( 'daemon_name', '', 'local2' );

    $message =~ s/\s+$//;
    syslog( $type, $message );

    closelog();

    return();
} # END syslog_event
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Then call syslog_event as needed passing it one of the allowed types and your message:

syslog_event( 'info', 'daemon starting' );
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The types are taken from the system types. Look in

man 3 syslog
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for 'level'. You'll see things like LOG_INFO, the type you need is everything after LOG_. You can use lower case if you like.

Phil