Kiffin did say he isn't withholding the name to create a competitive advantage against the Cougars.
Both Kessler and Wittek were informed of his decision Sunday in a meeting.
When pressed to provide any details how the decision was made and what went into the process, Kiffin stood firm, revealing nothing because he doesn't "want people outside our building tearing these guys apart."
"I'm not going to get into ‘this guy this' and ‘that guy that'," Kiffin explained. "We've made a decision and that's all I have. I don't want to hear a bunch of stuff that is going to affect these young kids. These are things we do within our team that don't need to be in the media."
The head coach did break down the performance of both quarterbacks in the Trojans season opening 30-13 win over Hawaii on Thursday. Though he left plenty of room to speculate around the breakdowns when it comes to guessing a starter.
Kessler in his first career start finished 10-of-19 for 95 yards, throwing one touchdown and one interception. He played the first half and the first series of the second half.
"I thought Cody started well his opening drive," Kiffin said. "[He] picks up a big third down and then makes a great throw to Marqise [Lee] on fourth down that he drops in a clutch situation and then he stalled out there and doesn't really have a good first half until the end. Then makes a poor decision on the pass he throws to the ground that was picked but ends the first half well. Some things for him to build on."
Wittek took over after Kessler went three and out to start the second half. He finished 5-of-10 for 77 yards.
"Max I thought had some good throws, really suffered from two long ball drops that I think, I know, if you put those two completions to him for another 80 yards it will be a very different numbers, so Max did well," Kiffin said.
Kessler and Wittek battled for the starting position through 15 spring practices, three weeks of fall camp, and game week. Through that time, Kiffin said he didn't think either quarterback separated himself until Kessler made a strong showing a few days before leaving for Hawaii, earning him the first reps against the Rainbow Warriors.
"I made the decision and we're going forward," Kiffin said. "That's all I got."
Based off the numbers from the game, it's anyone's guess who the starting quarterback will be – seeing as they were very close going into the game and had comparable numbers coming out of it.
The team will see for themselves who the new starting quarterback is when they take the practice field this week to prepare for Washington State.