At first Wayne Gallman thought it was “cheesy.”

It was a silly nickname, one that was almost too obvious to be considered clever. A big, physical running back named Wayne and they called him “The Train”? Surely there was something better.

But as time went on, Gallman started to appreciate his moniker. And when they started playing sounds of chugging locomotives and screaming whistles after his touchdowns and big runs at Clemson home games, it started to feel more and more comfortable.

Now, Gallman is on board with the name.

“I kind of just went along with it and accept it now,” he said.

And the Giants are all aboard too.

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They picked him in the fourth round with the 140th overall selection on Saturday. At 6-0, 215 pounds, Gallman adds a physical presence to their backfield that they have been lacking for several years.

“He provides a spark, a change-of-pace type,” coach Ben McAdoo said. “Has a lot of upside.”

The Giants wanted to add some beef to their running back room and had shown interest in signing former Patriots back LaGarrette Blount as a free agent. General manager Jerry Reese said the addition of Gallman will not preclude them from making such a move.

“We keep all our options open with respect to that,” Reese said. “There is a long way to go until we play.”

For now, Gallman will be in the backfield with Paul Perkins — the Giants’ fifth-round pick last year who emerged as the starter by the time the playoffs began — and third-down back Shane Vereen. The Giants released Rashad Jennings this offseason.

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“I watched [Perkins] in college and watched a couple games from New York last year,” Gallman said. “I know a little bit about their running game . . . I think I’ll be able to complement him and the offense well, as well as any other thing that they would want me to do. I’m just ready to come in and work.”

Gallman clearly believes he should have been selected earlier in the draft. Just moments after the Giants made the selection he posted on Twitter: “I promise . . . these teams will see my worth for years to come.” He said he was “shocked” when the Giants called, not because they did but because no one already had.

“I was hearing that I was supposed to go a little earlier than expected,” he said. “Just this way, I’m relaxing to it and trusted wherever I was going to go through God. When that phone call came, I was just shocked. I didn’t know who it was. I’m glad it was the New York Giants.”

The Giants selected 6-3, 264-pound defensive end Avery Moss from Youngstown State in the fifth round, a player Reese called “a true defensive end” with “a lot of upside.” It wasn’t until the sixth round that the Giants addressed what many believed to be their greatest need heading into this draft: an offensive lineman. That they traded up six spots, swapping sixth-rounders and giving their seventh to the Titans, illustrated that they thought 6-6, 305-pound tackle Adam Bisnowaty was one of the few draftable linemen remaining in what is considered a very lean class for the position.

“I’m a nasty football player,” Bisnowaty said. “I get after people . . . I make sure the guy across from me wants to quit.”

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He’s played mostly tackle at the University of Pittsburgh and he’ll start there, but the Giants think he might have some ability to move inside to guard as well.

“He’s a big guy, tough, rugged,” Reese said. “He’ll get with our offensive line group and challenge for a spot there.”