<p>Is there a <em>portable</em> way of getting thread and/or process identifier (string, int, ...) with C++?</p>

You have a few ways, but all imply the use of an external library abstracting the thread for you.
Among the popular choices, two are:
The
Boost.Thread
library. This is the most portable but imply working with Boost, which is a HUGE library
The
Qt
library. This is less portable and imply to work with Qt, a big library.
If you already use any on these two libraries, I would recommend sticking with it. Otherwise, look at what other tools they provide and make a choice.