This is what I could come up with after a quick search.
Admiral Vladivostok - Ziyavudin Magomedov (Summa Group)
Ak Bars Kazan - Tatneft
Amur Khabarovsk - Dalspetsstroy
Avangard Omsk -Gazprom Neft
Avtomobilist Ekaterinburg - ????
Barys Astana - KTZ
CSKA Moscow - Rosneft
Dynamo Minsk - BFSO Dinamo
Dynamo Moscow - Dynamo Sports Society
Dynamo Riga - ????
Jokerit Helsinki - Harkimo, Rotenberg, Timchenko
Lada Togliatti - AvtoVAZ
Lokomotiv Yaroslavl - Russian Railways
Medvescak Zagreb - ???
Metallurg Magnitogorsk - VIktor Razhnikov (MMK)
Metallurg Novokuznetsk - Evraz
Neftekhimik Nizhnekamsk - NKNK
Salavat Yulaev Ufa - Bashneft
Severstal Cherepovets - Severstal
Sibir Novosibirsk - ???
SKA Saint Petersburg - Gazprom
Slovan Bratislava - ????
Sochi - Gazprom
Spartak Moscow - Investbank
Torpedo Nizhny Novgorod - GAZ
Traktor Chelyabinsk - Chelyabinsk Admnistration
Vityaz Podolsk - ???
Yugra Khanty-Mansiysk - Khanty-Mansiysk Admnistration
Maybe Uraltransmash and NZHK-Instrument for Avtomobilitst and Sibir? Not sure.