Hi there,
Is there an easy way to log the names of the actual processes that initiate, let's say, outbound connections from the Linux machine, for instance track what process initiates an outbound connection to MySQL port to remote machine and stuff like that?

Thanks in advance!

Unfortunately - no.

Ok, thanks for clearing that out.
Is there any other way to do it without way too much hassle?
Thanks in advance!

Please try to be clear and avoid vague phrasing like "easy way", "stuff like that" and "without way too much hassle".

A process argv[0], its name, should not be considered as a selector. What is authoritative is that on a "clean" machine each process, however shortlived, will be visible in /proc. So, what you have related to processes are their PIDs and, in terms of filtering, the IP address of the remote machine and a remote port number. The only default Netfilter module that tracks process-related details directly is the "owner" module. Logging that information makes it available for further processing by any logwatcher. Since you didn't specify why you need to go through iptables I'd like to point out that there are other, possibly quicker, ways to get the information. If we assert that MySQL listens on its default port TCP/3306, then running 'netstat -tnpe|awk '/3306/ {print $NF}' will return the PIDs of processes using TCP and port 3306. But running 'lsof -t -P -w -n -i tcp:3306' should be even quicker. Having the PID you can find your name information in /proc/$PID/.* .