It was a memorable moment for Mariano Rivera III, but it was also a motivational one.

The Yankees selected the son of legendary closer Mariano Rivera in the 29th round (872 overall) last June, taking a chance on the late-blooming pitcher from Iona College. He was honored to hear his name called, but he also was far from satisfied.

He wanted more. He didn’t want to be considered a favor pick.

“In my mind I wanted to be a top 10-rounder,” Rivera III recalled. “I was set on coming back, no matter what. I wanted to prove to myself I can do this, I can do more. I wanted to see how far I could push myself and what I really could do with the talent and skills I have now.”

Rivera did return to Iona, and nearly a year later, is projected to go in the top 10 rounds, if not the top five. He is the Gaels’ ace, a hard-throwing right-hander with a 2.78 ERA, 90 strikeouts and just 20 walks in 71 1/3 innings, five complete games and two shutouts. Each start this spring has drawn between 10 and 15 major league scouts, cross-checkers and executives among them.

“One day I will be in the bigs and making a name for myself, and that drives me,” he boldly predicted.

Asked why, and the 5-foot-11, 155-pound Rivera said, why not have that belief, that confidence in himself? Few figured this was possible a few years ago, even Rivera himself. As a freshman, he recalled seeing a teammate hitting 88 mph on a radar gun, and wondering how he ever could throw that hard. An NL East scout recalled seeing Rivera throwing in the high 70s the summer before his freshman year of college. He was a mop-up reliever his first season, with a 7.25 ERA.

Now he is lighting up radar guns, topping out this spring at 97 mph, sitting in the low-to-mid 90s with his fastball.

“It’s almost like he reinvested himself,” said the scout, who has followed Rivera’s career.

“It’s a little bit hard to believe,” said Rivera, who graduates next weekend with an undergraduate degree in public relations, the first member of his family to do so.

Admittedly, the 21-year-old Rivera didn’t take baseball seriously until he got to Iona. Growing up in nearby Harrison, N.Y., he played for Iona Prep, but opportunities were scarce. His role was as a pinch-runner, sapping his motivation. He played summer ball with the Diamond Buddies, and Iona coach Pat Carey took a flyer on him, after getting positive reviews about Rivera’s strong arm. During workouts freshman year, Carey noticed Rivera’s throws from the outfield had “second life” to them.

“I’ve only seen that once before,” Carey said, back in his playing days at Providence College, from teammate Keith Reid, who would be a first-round pick.

Rivera doesn’t throw a cut fastball like his dad, he doesn’t wear No. 42 (No. 6 is his number) or have entrance music by Metallica, and he’s a starter for Iona, not a closer, but the two share one very important characteristic: their drive. Lost amid the father’s Hall of Fame career was the fact Rivera III wasn’t a highly acclaimed prospect. His father didn’t pick up his first save until the age of 25. He was a late bloomer.

“It was the same thing with the kid,” Carey said. “Just because he had his father’s name, he still had to earn who he was. Now he’s just put it all together. It’s been a lot of fun to watch.”

The elder Rivera attends his son’s games and the two will talk baseball, but briefly, focusing more on the mental side of the game. The great Yankee wants to stay out of his son’s spotlight.

But even he is impressed with how far his son has come, telling his wife Clara, “At his age he was throwing harder than me. He knows what he’s doing.”

“He gives me compliments behind the scenes,” Rivera said.

A major step in his development came this summer, playing for the Laconia Muskrats of the New England Collegiate Baseball League, one of the best summer leagues in the country, full of draftable high major Division I talents. There were times he struggled, days he was overmatched, and there were other times he excelled. One thing stood out to general manager Noah Crane.

“He wouldn’t shy away from a challenge,” Crane said. “You could see he had a purpose for the summer. He wanted to prove he was good enough to pitch at this level.”

Rivera was a fringe prospect last year, drafted on Day 3 by the Yankees. He doesn’t like to think of it as a favor, but knows that possibly was the case. That won’t be the result this year, whomever takes him. The NL East scout described him as a “legit prospect” who has piqued the interest of several teams because of his velocity increase, the action on his fastball and slider, and said the fact he has pitched only for a few years adds to his appeal.

“If he wasn’t the son of Mariano Rivera, he’d still be right where he is,” the scout said.

“He has made a lot of strides and has caught the attention of a lot of people,” another scout said. “The big thing about the velocity jump is that he is getting more strikeouts, and it has enhanced the slider which makes more people chase stuff.”

If Rivera goes in the top 10 rounds, as expected, he plans on beginning his professional journey, to start in earnest to carve out his own legacy.

“I’ll always have my father’s name,” he said. “That was the name I was given. I love that name. But I’m not my father. I want to make a name for myself. I’m fortunate enough to be doing this. It’s not him pitching on the mound, it’s me.

“I’m just beginning. It’s only going to get greater, hopefully.”

Additional reporting by George A. King III