I have noticed that the 4 Apostolic Patriarchates are on the internet quite often referred to as "Greek Orthodox Churches". I was wondering, what is the justification of this i.e. is there any official documentation for such naming?
For hundreds of years, depending on the time and place, all Orthodox (including Russians, Serbians, etc) were called "Greeks" or part of the "Greek church" or "Greek Orthodox" or celebrants of the "Greek rite." That's how Westerners had referred to Orthodox since at least the 9th century, and, at various times, the Orthodox adopted the nomenclature as well. Hence why Metropolitan Platon of Moscow's book was translated into English in 1815 as "The Present State of the Greek Church in Russia."
When it comes to today's discourse on Internet, the patriarchates in question are called "Greek" because they follow "Greek," i.e. Byzantine liturgical traditions, as opposed to the other liturgical traditions that have evolved in Russia, Serbia, etc.