The most valuable source of information is white pages (phone directories), many of which are available online. Most large cities of Ukraine and Russia have such electronic directories, whilst in the US, Canada and some other countries you can search across ALL phone numbers of a country.
Besides, there are many search engines and specialised genealogical databases.
Kosarenko can be found most frequently in Ukraine, of course: 15 numbers in Kyiv, 5 in Odesa, 4 in Mariupol', 4 in Dnipropetrovsk, 3 in Kharkiv, 1 in Chernihiv, 1 in Kherson, 1 in Lviv. I could not find white pages of several other cities (Donetsk, Kryvyi Rih, Zaporizhzhia, Mykolaiv, Makiivka, Horlivka).
From non-phone-related Internet sources, we know that Kosarenko lived or still live in Zaporizhzhia, Sumy, Khrystynivka of Cherkasy region.
In January 2000, I polled twelve Kosarenko from Kyiv. Apparently, they originate predominantly from
Obviously, one can not apply this scheme to large cities, where Kosarenko could appear and disappear independently from the historic movements of Ukrainian people. I mean Moscow and St.Petersburg in the first place.
Outside Ukraine, the most of Kosarenko live in Russia. In Moscow, there are 12 phone numbers under such surname. Apart of that, there are or were Kosarenko in St. Petersburg, Arkhangelsk, Kaliningrad, Tver, Voronezh, Rostov-on-Don and Rostov region, Astrakhan, Cheliabinsk, Kemerovo, Omsk, Tumen' region, Krasnoyarsk.
There are Kosarenko in Belarus (Minsk, Grodno), Kyrgyzstan (Bishkek). Outside the former USSR - in Yugoslavia (Novi Sad), Germany (Passau, Windsbach), Austria (Wien), Canada (Toronto, Montreal, Mississauga, Winnipeg, Brampton), USA (New York, Detroit, San-Fransisco), Argentina.
I know that ancestors of some of those Kosarenko emograted in the beginning of the XX century. One Canadian family originates, according to the family legend, from town Stryi, which they left in 1903. That is a surprise itself, as the surnames of this kind are not typical for Western Ukraine.
Overall, Kosarenko left their home villages decades ago, before the Russian revolution of 1917.