WEST POINT — Knicks rookie small forward Mindaugas Kuzminskas has an intriguing nickname from his friends back in Lithuania. While Phil Jackson has branded him “Kuz,’’ his buddies have a niftier one.

“It’s ‘Cheese,’ ’’ Kuzminskas told The Post after practice this week. “I’m smiling all the time almost. When you take a picture, you say ‘Cheese.’ That’s my nickname.’’

Kuzminskas, 26, has plenty to smile about now. Undrafted in 2011, the 6-foot-8 swingman signed a three-year contract with the Knicks in July starting at the $2.8 million cap-room exception. His introductory trip to New York came in July to sign the pact before he rejoined Lithuania’s Olympic team.

“I watched a lot of movies before, so I saw New York on movies and pictures,’’ Kuzminskas said. “I had a feeling like in ‘Home Alone,’ going to the hotel, walking between skyscrapers.”

The sharpshooting blond is penciled in as Carmelo Anthony’s backup at small forward after he averaged 10.8 points and 4.5 rebounds in 22 minutes per game in the Olympics. Lithuania lost in the quarterfinals to Australia, so Kuzminskas did not meet Anthony until arriving in New York for voluntary workouts in early September.

“When I got here, he asked me right away how was the Olympics and about my team,’’ Kuzminskas said. “Such a big player to know something about me, I felt immediately better on the team. Every day I pick up something from him, defending him at the practices are unforgettable, priceless.

“It’s really exciting to be here with these players, to practice every day against my position players — Carmelo, Lance Thomas. Great lessons and huge experience that will help me in the future.’’

Jackson has hailed Kuzminskas’ perimeter shooting, saying he can even turn into a shooting guard. The Knicks president still is concerned about his strength. Kuzminskas played the last three seasons for Malaga of the Spanish League.

“He’s going to be a process, but we like what we see,’’ Jackson said.

“I like a fast game, a lot of movements, I try to dive for every ball, to play smart,’’ Kuzminskas said. “Maybe guys from Europe are not the best athletes. You just need to use your brain, movement, and try to help the team in that way. It’s really important when on NBA and national teams to find your role on the team. Guys are usually the best players on their European team before they come into the league. You got to find a role to help the [NBA] team another way.’’

His on-court intelligence and movement without the ball, a key to the triangle offense, have won over coach Jeff Hornacek.

“He’s a guy that with his size, got agility, you can look at him at the 2 or 3,’’ Hornacek said. “There could be times we use his length at the 2 spot. He’s a guy who cuts — cutters open everything up. The stat’s not in the paper. You don’t get glory from it but it’s a huge part.’’

Asked if he feels he has proven he deserves a rotation slot, Kuzminskas gave his oft-present smile.

“I can’t talk about that,’’ he said. “It’s better when other people talk from the side, you can see better. I’m kind of a shy guy. It’s my first year. There are a lot of opinions. The coaches want to win, so they’re going to use the players most ready at the moment.”

Kuzminskas, who speaks English as crisply as does Kristaps Porzingis, believes the Olympic experience was a blessing leading into his rookie year.

“It was great for our little country,’’ Kuzminskas said. ”It’s a huge thing. It’s really hard to make it for us. We lost quarterfinals, but it was my first Olympics and I hope it was not the last one, to live in the Olympic Village to walk between the best athletes. You see Michael Phelps and Novak Djokovic, then you feel really special and understand the importance of the Olympic games.’’

The Hawks and Lakers were his most ardent suitors.

“I wasn’t surprised,’’ Kuzminskas said of not getting drafted. “It’s much harder to be drafted when playing in Lithuania when playing for example in Spain. You don’t have too many teams and scouts. I’m a late bloomer. Right now I think it was a good thing I wasn’t drafted. I played good seasons in Europe and [was] able to choose different options.’’