Does Putin have a Dick Cheney (as G.W.Bush did) or a Steven Bannon (as the current head of state does) to tell him what to do?

From the books I've read? Putin is under the control of the rich Oligarchs. He is actually their puppet as they have all the money and power and Putin will do as their council says. He doesn't have the power that people think that he does. If he didn't do as they wished? He would disappear and someone new would show up.

Oligarch : 

1. a ruler in an oligarchy.
2. 2.

   (especially in Russia) a very rich business leader with a great deal of political influence.

I expect there are many "would be" secret rulers like that, normally most of them fail.
Whether they are "good" or "bad" would depend on the agenda they are secretly pushing. Dick Cheney pushed PNAC (a triumphalist idea that now the USSR was out of the way the US should take up the reins it so obviously deserved and rule the world (PNAC is an acronym for Project New American Century)

So if Putin have someone like that, then it is probably a smarter one. One more likely to base his speculations on known facts instead of wishful dreams.