Remote labeled log

[lzkill]

Hi folks.

I'm using Papertrail for remote logging, but since I live under a dynamic connection it gets really messy. My ISP changes my IP every 48 hours, so Papertrail adds a different system for each different IP.

Jan 28 16:31:09 187.59.98.217 dropbear:  Pubkey auth succeeded for 'admin'
Jan 28 16:38:14 187.59.98.217 dropbear:  Exit (admin): Exited normally 
Jan 28 16:46:47 rpi sshd:  pam_unix(sshd:session): session opened for user pi by (uid=0)

How can I make syslogd to log events labeled with the hostname, like my rpi does? (it runs rsyslog)

Thanks in advance!