Rosen, who began classes at UCLA on Jan. 5, chuckles when asked about nicknames.
"My buddies mess around, call me 'Chosen Rosen,' " he says. "Our student section would chant it every now and then."
Rosen tries to keep the hype that surrounds him in perspective. "You can't really look too much into what everyone has to say about you," he says. "When you try to please everybody, you please no one."
Hundley's departure — he has announced he's leaving UCLA a year early for the NFL — leaves a gaping hole on a team that expects to have 18 of 22 starters return. At quarterback, the Bruins would have Jerry Neuheisel, who will be a fourth-year junior next season, as well as third-year sophomore Asiantii Woulard and fourth-year junior Mike Fafaul. Neither Woulard nor Fafaul threw a pass last season, and Neuheisel had a big moment in a victory over Texas.
Rosen, who was ranked at or near the top among senior high school quarterbacks in the nation, enrolled at UCLA early so he could participate in spring practice and be ready to compete to be the Bruins' starter during summer camp.
He is aware his every move will be studied.
"Everyone is going to be looking at me to see how I react to the first time I get yelled at," Rosen says. "They are going to want to see how I react to the first time I get told to do something. If I put effort into everything I do around the team, I can earn their respect."
You could say Rosen was born to play quarterback and not be too far off, his family says. As a baby, he tossed bottles from his crib at his mother, Liz Lippincott.
"Apparently, I hucked bottles all over," Rosen says.
And other things.
"We were playing horseshoes and he hurled one and hit me in the temple," Lippincott says. "I should have bought those soft horseshoes."
Yet, when it came to sports, tennis was Rosen's first love. "When he was 4 or 5, he thought it was the only sport on the planet," says Lippincott, who had played tennis competitively.
Rosen was a top-10 player in juniors rankings, but football eventually took over after he was introduced to the sport while in elementary school by a friend whose father was a youth coach.
"I think he realized that on the national level playing tennis meant home schooling and racing around the country on airplanes with his mother," Lippincott says.
By the time Rosen reached high school, he had earned a reputation as "a very competitive guy" who was "always looking for a challenge," says Jaleel Wadood, a UCLA defensive back who was a teammate at St. John Bosco.
Quarterback was a fit for his personality.
"He wants to be in control of everything, in the house, outside the house, at school, on the field," Lippincott says. "He wants to say, "I mastered it, I understand it.' "
Rosen was St. John Bosco's starter for three seasons, passing for 11,175 yards and 90 touchdowns.
"It was pretty obvious the kid could throw the football," UCLA offensive coordinator Noel Mazzone says. "The more I watched him play, the more I realized he had a great understanding of the game. He gets it."
Beyond the gaudy statistics, Wadood says Rosen "knows how to win."
In 2013, St. John Bosco had a record of 16-0 and finished the season as the top-ranked high school team in the nation.
When it came time to pick a college, there was really no second choice.
Last spring, when Rosen formally announced his destination, he brought three baseball caps with him — all of them from UCLA.
His arrival on campus last week was noted by
Rosen seems well aware that pressure comes with fame, and he has priorities. "At the moment, I just want to get acclimated as a college student," he says.
Quarterbacks rarely earn starting jobs as true freshmen. Hundley didn't, sitting out as a redshirt in 2011.
The only first-year freshman quarterback to start for a national championship team was Jamelle Holieway, who in 1985 took over for an injured Aikman in the fourth game and led Oklahoma to the title.
Rosen comes to UCLA at least partially polished. "He has a pretty good background," Mazzone says. "There are a lot of similarities with what St. John Bosco does and what we do. He's not on Floor One."
He'll have competition, though.
While Neuheisel does not have Hundley's athletic skills, he does have "everything you need to win in this offense," Mazzone says. Neuheisel is also game tested. He came off the bench in September after Hundley was injured and led UCLA to a 20-17 victory over Texas.
Whoever wins the job will have a strong supporting cast. The Bruins are expected to return the entire offensive line and every prominent receiver, plus Paul Perkins, whose 1,575 yards rushing led the Pac-12 Conference.
The bar for UCLA quarterbacks was set higher by Hundley.
Before he arrived, UCLA had not had a quarterback play in every game in a season since 2005. Hundley didn't miss a start in three seasons in passing for 9,966 yards and a school-record 75 touchdowns.
"We've made big time strides from where we were three years ago," Hundley says. "Josh is coming in with the program on the rise."
Rosen has listened carefully to what Hundley told him about making the transition from high school to college.
"Nothing is going to be as you imagined or as easy as you think," Hundley says. "It's a major learning curve that you have to get to really quick."
Rosen isn't a Hundley clone. They have different strengths and styles.
Hundley was a runner, finishing with 1,747 career rushing yards, second-most by a UCLA quarterback.
Rosen is mobile, but is much less likely to tuck the ball under his arm and head downfield.
"He does it his way. I'll do it my way," Rosen says. "I don't plan on running the ball as much. I definitely want to use my incredibly dedicated, large and determined offensive linemen to protect me. I'll get the ball to receivers and let them do their thing.
"If," he adds, "I win the job."
Yes, first things first. Although Rosen has already thought about what he'd like as a legacy.
"I want to be a good guy who won football games," Rosen says. "I want to push them over the heap and get them a national championship."