こく becoming ごく is called rendaku! There are some patterns to this, but of course, there are also plenty of exceptions! My understanding is that it generally happens primarily to kun’yomi readings (so 国 is an unusual case), and typically it’s the second kanji that does it, but there are circumstances that stop it from happening, plus occasional irregular readings that break the rules, haha!
I haven’t actually done any formal investigating into this yet myself, but I’ve picked up a lot of the patterns just from using the rendaku information script and reading the rendaku section for each new vocab word that I learn. A lot of the stuff in the script went over my head at first, but the longer I’ve had it installed, the more I’ve begun to get a sense for the patterns. Of course, you can pick up on a lot of this eventually without using a script, but the script is nice because it directly spells out what is happening, so it helps you conceptualize it better.