Irishman Barry Fox may feel a little like his namesake -- a small business critter about to be hounded out of the television business by Rupert Murdoch's megamedia conglomerate.

About six years ago, cameraman Fox started his own television production company "with my right eyeball," which is the way cameramen talk. He also had a bank loan and a corporate name -- Fox Television.

Now he has 11 camera crews that he rents primarily to American broadcasters, lending a technological hand to NBC's "Today," ABC's "Good Morning America" and "Nightline," CBS, CNN and the "MacNeil/Lehrer NewsHour," to name a few.

Last year, while Fox was doing about $1.2 million in business, Murdoch bought half of Twentieth Century Fox Film Corp. for $325 million plus real estate. He then combined his film arm with his six Metromedia television stations (worth $1.5 billion) to try his hand at building a fourth network. He called it Fox Television Stations, known fairly commonly as Fox Television.

"It really is like waking up one morning and finding out somebody like the BBC has decided to call themselves by your name," Fox told The Post's Karen DeYoung in London.

So Fox, who incorporated in London in 1980 and in the United States in 1983, has sued Murdoch in two courts -- the High Court in London and the Supreme Court in New York.

In this country, Fox asked for $30 million and an injunction against the use of the name Fox Television. Murdoch has counter-sued, asking for $1 million and an injunction against Barry Fox for using the name Fox Television.

New York Supreme Court Judge Martin Evans denied both injunctions until a trial that is expected to start June 23. Murdoch's lawyer, Howard Squadron, could not be reached but has contended that the 20th Century Fox Television Division established the name as its own.

Until a court decides, however, there will be the big Fox Television and the little Fox Television, a confusion that sounds like a children's book to everybody but the owners and their lawyers.

Fox, who hoped to do $2 million in business this year, says that the amount of money going to attorneys "is just horrific, but then I've got to match that against the losses . . . It's created something slightly more than a simple problem for me." The Birth of fathers

Out of joy, suffering, a good deal of doubt and even more enthusiasm, fathers magazine has been born.

This newest publishing offspring of Editor Harry Stein, formerly of Esquire, and President Jeff Stein, formerly of Washington Weekly, hits the newsstands today. In a marketing gimmick that certainly would not have been considered by many of the magazines for supermothers, there will also be a copy on every seat at Joe & Mo's restaurant.

"It will be a lot different from those magazines," Managing Editor Duncan Spencer said yesterday. "We will not put in any studio pictures. There will not be a lot of pretty faces like the ones you see on the cover of every women's magazine. They all say how you too can be as beautiful as she is, and therefore as successful and wondrous. We've decided as a policy to only use photographs of real people doing real things and to try to deal with the realities of fatherhood rather than an image."

The maiden issue, if you will, features a young Ronald Reagan with his small son Ron on the cover. Inside Ron tells what it's like to be his father's son -- including facts about how Reagan feels about alcohol ("He likes wine; he collects wine"). Ron says that he talked more with his mother, the first lady, about Reagan's first wife Jane Wyman than he did with his father. "He was totally hurt by the whole thing," says young Reagan.

The issue also includes a story on sons of baseball players, best books for bedtime reading, a crash course in strollers and mini-interviews with famous people about fatherhood.

Says writer Larry L. King, who has two families: "I try to teach them honesty, you know. But truthfully, there's just damn little you can teach them. Some kids just turn out sorry as puke no matter what." Adding that he loves his kids, King says he is irritated by those who say "kids keep you going" -- "what a load of horse manure . By Friday night our nanny is stark-raving mad. Absolutely insane."

The first issue, of which about 25,000 copies have been printed, also includes a reputable cast. Among the contributing editors are Ken Auletta, James Fallows, Dan Greenburg and Dana Andrew Jennings. Peter Ross Range is senior editor, and Reed Phillips, who has been assistant publisher of The New Republic, is the new publisher.

Money for the daring venture has come from the Steins (who are not related), Phillips and other investors, including Dr. Charlie Clements (subject of the Oscar-winning documentary "Witness to War"), Spencer and Spencer's sister Margaret Douglas-Hamilton (who runs Hamilton Equine Systems, a sperm bank for horse breeders).

Editor Stein, speaking from his home in Westchester County, N.Y., said he wanted the magazine to shed the tone of "deadly earnestness" that many magazines have used to describe the joys of fatherhood. As he talks about fathers magazine, he stops for a minute to talk to one of his two children.

"I can't play baseball now, darling," he says, then continues rhapsodizing about a magazine dedicated to the male parent. The News on Chernobyl

The media fallout from Chernobyl has included a few journalistic cleanup brigades, righting wrongs, adapting to new news and even searching for new areas of concern.

Perhaps most notable was that UPI, which reported shortly after the April 26 accident that 2,000 had died, unreported that fact almost a month later on May 22.

In a classy retraction of a story that had been used by clients of the wire, editor in chief Maxwell McCrohon said that "subsequent developments have not confirmed the report, and it appears UPI was misinformed for reasons we have been unable to determine."

UPI's source said in a letter to two Soviet news outlets that she had said two, not two thousand, a miscalculation that UPI denied.

By contrast, there is no word yet from the New York Post, whose May 2 headline screamed: "Mass Grave 15,000 N-Victims."

The Chernobyl story goes on, and The New York Times, which has featured plenty of strong and generally excellent news coverage of the event, also apparently took time to look at other sides of the issue.

A memorandum from The Times' Paris stringer, which came into the New York computer on its open lines, was widely read among even the most unskilled hackers in the paper's New York newsroom, and Geoffrey Stokes of The Village Voice reprinted a version of it this week that Times sources confirmed is correct.

Addressed to Arthur Gelb, deputy managing editor of The Times, the memo said in part: "I've thoroughly checked into the situation on 'radioactive' caviar, foie gras, snails, frog legs, etc. For many reasons, there is no big story here . . . If the nuclear disaster had occurred before Christmas time, when about 80 percent of the foie gras is imported and consumed, it would have been another story. Also, am pretty well convinced that the caviar is safe, for the spring catch was in the tins at the time of the disaster . . . "