Okay I just finished my first playthrough of Inquisition. I wanted to make Leliana the new divine and I remember saying to her that I would support her. I didnt say anything like that to the other candidates. The epilogue still mentions how Vivienne came the new divine even though she was the last person I wanted to become that so I wasnt happy.
How do you make sure the person YOU want to become the new divine, becomes that?
You basically have to agree with all of Leliana's views throughout the playthrough. This means when talking to Casandra at one point, " You tell her the Chantry has failed" or when talking to Vivienne you tell her "You believe all mages should be free". These choices in dialogue have just as much as an effect like the decisions to side with the mages or templars. It really doesn't matter who you support at the end( although I hear having max influence does help whoever you decide to support, but only really if you have max influence). It all comes down to your stances and what you say/do throughout the game.
There are some walkthroughs on youtube that guide you in getting whoever you want as Divine.