How can I know my current Photoshop color profile?

One can also set the Info Panel to display »Document Profile«. 

But the Status Bar @davescm mentioned seems particularly useful. 

At the bottom left of the Photoshop document window, just next to the displayed zoom level is a little information about the document. If you click the small arrow next to it you will see a menu and you can set it to Document Profile. That way you can see at a glance the profile of the open document.

Dave