dhcp-relay custom log file

You can't. What you can do is make syslog log that to a separate file (see /etc/rsyslog.d/).

• Create file /etc/rsyslog.d/dhcp-relay.conf
• Add the line local7.* -/var/log/dhcp-relay.log
• restart rsyslog

Also look at the file /etc/rsyslog.d/50-default.conf, maybe you want to change the line where it logs to /var/log/syslog to contain local7.none to avoid double loggings.