Is Howard Stern Jewish?

Yes, Howard Stern is a Jew and his Hebrew name is Tzvi.  Here is Wikipedia, saying he calls himself "half-Jewish."

Howard Stern was born on January 12, 1954 in Jackson Heights, Queens in New York City. His parents Ben and Ray Stern (née Schiffman) are children of Austro-Hungarian immigrants. Ellen, his elder sister of four years, is described by Stern as "completely opposite" though they maintain a good relationship. Though born into a Jewish American family (his Hebrew name is "Tzvi"), Stern claims on the radio that he is just "half-Jewish". Five months after Stern's birth, the family moved to the suburban area of Roosevelt on Long Island.

As E Online reports, Howard does not like Jay Leno.

Don't mention Jay Leno to Howard Stern unless you have a paper bag handy.

"Just the mere mention of Jay Leno's name makes me want to vomit," the shock jock told Harry Smith on CBS' Early Show this morning. "I don't like this guy. I don't disguise it. Probably what irritates me the most is people in show business are afraid to say how much they dislike the guy, but I am not."
Clearly, the Sirus XM radio king remains on Team Coco, supporting Conan O'Brien even after NBC's dirty dealing was done.

"Jay completely sabotaged him," Stern ranted. "By going on at 10 o'clock, they gave Jay all the best guests, it took away all of Conan's excitement and thunder...Jay is a lap dog...Jay should have dusted himself off, gone to another network. He certainly had the offers."

In addition to accusing the large-chinned-one of "pushing Johnny Carson out of The Tonight Show...in a merciless way," Stern accused Leno of plagiarism, while applauding David Letterman.

"Jay is also a thief, and that's what gets me," Stern said. "That's what gets my goat the most. You know, I've always considered myself an original. I consider Dave an original, David Letterman. I think he’s a pioneer. David Letterman once said in an interview—he started putting his mother on the air—and he said, you know, 'I got that from Howard Stern.' I admire that. Jay takes and lifts bits directly from my show, directly from Dave’s show...They don’t have an original thought on that show."

Yowza!