DAD ASIDE, IT'S ADAM'S TURN.

Byline: Fred Shuster Daily News Music Writer

Some say Adam Cohen only got his record deal because he's the son of rock icon and poet Leonard Cohen.

Surprisingly, though, the 25-year-old Cohen doesn't really mind that perception. In fact, he's thankful for any attention paid to his music, regardless of the reason.

``You don't get a record deal until the company feels it can make a buck off you,'' he said. ``The fact that I am who I am has definitely raised an eyebrow, but I've benefited from that.''

The well-mannered, thoughtful Cohen is as comfortable talking about his dad as he is discussing the Greek islands, one of several places - along with Canada and France - where he grew up.

Cohen's self-titled debut was released this week by Columbia, his father's longtime label. The disc was produced by Leonard Cohen producer Steve Lindsay, with backing from high-profile session musicians such as guitarists Dean Parks and David Baerwald, bassist Larry Klein, and drummers Jim Keltner and Matt Chamberlain.

``You're always taught to be suspicious of the record company, but the label you end up knowing the most about is the one you hear the most about from your pops,'' Cohen said.

Cohen co-wrote all of the album's 12 tracks, including six with Phil Roy and three with Tonio K. The material ranges from the catchy pop of ``Tell Me Everything'' to the sweet ballad ``Beautiful as You'' and the bitter ``Quarterback.''

Tom Corson, Columbia's senior vice president of marketing, says Cohen is an artist in his own right, despite his background.

``Anyone that says he got signed because of his dad hasn't heard the record or seen him perform,'' Corson said from New York. ``He's a musician and personality. As people get to know him, they'll find he exceeds expectations.''

For his part, Cohen isn't shy about discussing his father's influence.

``He's given me a high standard by which to live,'' Cohen said. ``I've definitely inherited his sensibility. He's given me so much.''

Before moving to Los Angeles, Cohen fronted a band in New York with Chris Stills, son of Stephen Stills. Other friends include Rufus Wainwright, son of Loudon, and Teddy Thompson, son of Richard.

``The music business today is frightening,'' Cohen said. ``There's a real battle between art and commerce that's being lost. It's tough to battle commerce because it's the instrument by which art gets discovered these days. I'm trying to infuse a commercial sensibility to my music while at the same time not compromising.''

Cohen was primarily raised by his mom, Suzanne Elrod, pictured on the cover of Leonard Cohen's 1977 album, ``Death of a Ladies Man.'' Yet, the younger Cohen says his father made an effort to spend time with him.

As for the spate of recent articles lumping together the newly signed sons and daughters of rock icons, Cohen says it also doesn't bother him much.

``It's OK with me,'' he said. ``By putting us all together, it almost sets up a tone of solidarity that I'm not averse to at all. To resist is to fuel people's intrigue.

``Like Jakob Dylan's disinterest in speaking about his father is the main catalyst for people wanting to speak exclusively about that.''

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Photo: Adam Cohen: ``The fact that I am who I am has definitely raised an eyebrow, but I've benefited from that.''