Drew Brees set an NFL record in 2011 for passing yardage. (Wade Payne/Associated Press)

— Late last month, when it came time for the New Orleans Saints to name their third head coach this year — technically, the interim-to-the-interim-head-coach — there appeared to be one primary consideration. Which assistant coach could do the job with the least amount of disruption to the daily operations of a team that has already experienced more disruption than any franchise in recent memory?

And so, in selecting the fill-in for Joe Vitt, who was himself the fill-in for Sean Payton, the Saints bypassed their two coordinators — one of whom, defensive coordinator Steve Spagnuolo, was just eight months removed from the head coaching job in St. Louis. They named offensive line coach Aaron Kromer to the interim-interim gig. Kromer, who will lead the Saints for the first six games of their season, beginning with Sunday’s opener at the Superdome against the Washington Redskins, saw the move for what it was.

“I’m the fill-in for the fill-in,” he said. “And I’m going to do the best job I can do.”

What is abundantly clear about the Saints is this: It hardly matters who coaches them anymore. For one thing, Payton’s program — from the schedules of his practices, to the in-game play-calling, to the seating chart on the team plane — is so deeply ingrained in the Saints’ culture, after six years of his regime, that it can basically operate on auto-pilot, while Payton serves his one-year suspension for his alleged role in the Saints’ “Bountygate” scandal.

“Tell me the difference between last year’s training camp and this year’s training camp,” Kromer said. “Tell me the difference you see in the way we do things, the . . . plays we run, the hustle, the tempo on the field. There isn’t a difference — because we’re following what Sean Payton has taught us. It’s his program. It’s the way he’s done it, and we’ve had a lot of success doing it that way.”

For another thing, the Saints still have Drew Brees, who increasingly seems indistinguishable from Payton, himself a former quarterback.

“They’re kind of the same person,” laughed Saints guard Jahri Evans, a first-team all-pro pick in 2011, speaking of Brees and Payton. “So we’re lucky to have [Brees] already in place at a time like this.”

Close your eyes as Brees is speaking, and you would be hard-pressed to discern whether the voice is his or his coach’s. After 12 years in the league, including the last six under Payton, Brees has perfected the unique brand of NFL coach-speak, and never has it been on more vivid display — or more comforting, given the Saints’ upheaval — than this summer.

“People don’t realize the type of men we have in this room — a lot of veterans, a lot of guys who’ve been here a long time,” Brees said recently at his locker at the Saints’ training complex outside New Orleans. “We know the way to do things, what’s expected of us, and everyone who comes here as a rookie or a free-agent kind of falls in line.”

It is Brees’s presence, above all, that has brought comfort to the Saints in the fallout from Bountygate, the nickname for the NFL’s conclusion that the Saints had paid defensive players cash bonuses to injure opponents. NFL Commissioner Roger Goodell levied steep suspensions against Payton (full season), Vitt (six games), linebacker Jonathan Vilma (full season), General Manager Mickey Loomis (eight games) and defensive end Will Smith (four games). Two other players now with other teams were also suspended.

There were, however, some anxious moments in New Orleans before Brees signed his five-year, $100 million contract extension in mid-July, ending a standoff that had lasted months.

“There’s no question, when Brees got signed and came in here,” said punter Thomas Morstead, “it was like, ‘Okay, our leader’s here — let’s roll.’ ”

Brees, who set an NFL record in 2011 for passing yardage (5,746), has long been treated as a de facto coach in New Orleans, enjoying a level of input — in everything from the playbook to the practice schedule — that is perhaps unparalleled in the league.

“Something I’ve always been humbled by, and take as a big responsibility is the fact I do get asked my opinions a lot in regards to . . . big decisions,” Brees said. “I appreciate that. Even if it’s just to give my input or my take, or in a lot of cases, Sean Payton will call me aside and say, ‘What’s the pulse of the team right now? How’re the guys feeling?’ I appreciate that, and I obviously try to give the best input I can.”

When the Saints reported for training camp this summer — launching their mission to become the first team in history to play a Super Bowl in their home stadium — they discovered an enormous poster of Payton’s face hanging from the rafters at the indoor practice facility, bearing one of his favorite slogans: “Do your job.”

It was a reminder of both Payton’s spiritual presence with the team, despite his forced absence, and the importance of continuity for a franchise that has won 41 games the past three seasons, including Super Bowl XLIV. No team in the NFL boasts a coach-quarterback-GM triumvirate that has been together as long as Payton, Brees and Loomis.

But with Payton gone, somebody else has to do his job. While Kromer and Vitt will handle the official duties, the team’s unofficial interim coach — if defined as the person most equipped to fill the leadership void — might just be the fellow wearing black-and-gold uniform No. 9.