That would absolutely work. It sounds easy and it doesn't take up any screen real estate.

I have added this request to the tracker:
Issue 2171 – Display IP address of the server
You can vote for it there.

For a start, what about adding the IP address to the hint window that shows when hovering over the session tab?

I too think this would be nice. When connecting via domain name, showing the IP address will let me know if I have connected via IPv4 or IPv6 (without having to consult a log file)

Thanks for your suggestion.
We will see, if more people ask for this.

Is it possible to have the IP address in the top bar along with the hostname as an option?
Sometimes it can be difficult to see what's going on, obviously you can have the IP in the name but handy to have it as an ON/OFF option.