Not long ago Walter Washington received a call from a woman complaining that there was too much fat on the meat at her neighborhood grocery store.

Washington politely informed her that there was little he could do - even if he were the Walter Washington she had intended to call. As it was, she had reached Walter Washington, retired Bureau of Standards employee, not the mayor.

Like most who bear the name of a famous person, Washington, who lives in Northeast, hears from all kinds of people he doesn't know at any time of the day or night. "When there was a disturbance at the District jail, people called me," he says. "I didn't know anything about a disturbance. But I guess I got the word before Mayor Washington did."

People with big names learn to live with a lot: the weirdo phone calls, the worn-out jokes ("Sure you're Jimmy Carter . . . and I'm Joseph Stalin, heh heh.") One frustrated John Dean changed his name legally to Natty Bumppo.And some take refuge in nonpublished phone numbers, prefering inconvenience to harassment.

One classic case of mistaken identity in Washington involves two John Siricas. "He's the judge and I'm the artist," says John Clemente Sirica, who heard from "crackpots" and "drunks" among others during the Watergate trial. Recently, when the judge announced his retirement, "I got calls from California, New York - all over," says Sirica, the artist, whose work sometimes is displayed around the city, leading some to think the judge is an artist.

"I called him after his heart attack," says the artist, who says he is a "distant cousin" of the judge, "and told him he was getting a hell of a reputation as a print-maker."

Unlike the Siricas, Richard Helms and Richard Helms have never spoken. But the Air Force master sergeant at Bolling Air Force Base sometimes gets two or three calls a week intended for the former CIA director. Sometimes, the master sergeant gets calls from Iran, where the better-known Helms served as ambassador.

The sergeant says he's never gotten an unpleasant call for the other Helms, although "There was one weird one. It supposedly came from California and he pretended he was Richard Helms. He wanted to know if I had had many problems because of my name. But I could tell it wasn't Richard Helms. He had a fairly young-sounding voice. I asked him some questions he didn't know the answers to. Then he hung up."

The sergeant says his wife has received calls about invitations to social events obviously meant for the other Mrs. Helms, "for some dinner, or something like that. I told her she ought to accept some of them sometime."

Invitations also come to the home of Arthur F. Burns of Silver Spring. "We get engraved invitations from government agencies to attend parties," says Sherry Burns, wife of an Arthur who is not the outgoing chairman of the Federal Reserve Board.And her husband get calls asking, "Is this THE Arthur Burns?"

Ronald McDonald, a real estate man in Adelphi, says that when he is introduced to children "their eyes get real big and they ask. 'Where's your clown suit?'" He says he's gotten calls from youngsters, small ones who've just learned to read and dial, trying to reach the clown.

Then there's John Lindsay, a Washington correspondent for Newsweek, who's had a taste of the lifestyle of John Lindsay, former representative and former mayor of New York.

"When he first came to town as a congressman, I'd get calls from his kooky constituency and he'd get my letters, which were just as bad, I might add," says Lindsay, the correspondent.

Things didn't improve after the representative had become mayor. Journalist Lindsay says that when he would check into a New York hotel while visiting Newsweek's home office, "two things would invariably happen as soon as I left my name at the switchboard for incoming calls: There would be a basket of fruit in front of my door, or all the services of the hotel would be shut off to me immediately."

Similarly, Newsweek's Lindsay says that while he was covering the 1972 Democratic Convention in Miami, the year Lindsay the politician had made a brief run for President, he was jolted from sleep by a phone call to his room. "It was like 5 after 4 in the morning, just after all the bars had closed, and this guy was all over Lindsay.I got a real insight into how beloved the mayor was in certain sections of New York."

Around Washington, Elizabeth Taylors are a favorite target. Possibly to counteract this, one Elizabeth Taylor in Virginia has gone to a nonpublished number. (Other phone book dropouts include John Wayne in Maryland and a Byron White in the District.) But the man who now has the old Taylor number says he gets "about three or four calls a week" for Elizabeth Taylor and will be happy when the new phone books come out.

But another Elizabeth Taylor, a 71-year-old Washington Woman, says she hasn't gotten as many calls recently as she used to, and none from anyone thinking she's the actress. Usually, it's "like when high schols are having initiations, that kind of thing . . . people thinking it'd be fun to call . . . Two in the morning, that's annoying. I just live with it."

The arrival of Jimmy Carter in Washington changed the life of Jimmy Carter, a carpenter in Arlington. "We get a tremendous number of calls," says the Arlington Jimmy's wife, Bonnie. "Especially the first two or three months after the inauguration. Some of the people honestly thought that our President would have his private phone number listed, which was unbelievable . . . People wanted to know if their children could play with Amy."

Mrs. Carter says now most of the calls involve jokes - "Over 90 per cent have to do with the peanut industry" - and that there are other callers who persist in talking, forcing her to hang up or take the phone off the hook. But she says she'll keep the number because their children are used to it and because they've had it since before they even heard of the newer Jimmy Carter in town.

Sometimes having a famous name can be beneficial. "One restaurant sent me a ticket for two dinners," says Larry Omega Brown, who is always being confused with Larry Brown, the former Redskin. "I kept them and had dinner. When I got there they were disappointed it wasn't the football player, but there was nothing they could do. Great dinner."

Not even the death of a famous personality can still the phone. Jesse James and Ty Cobb, both of Northeast, and Howard Hughes of Prosperity Avenue, Fairfax, are forever getting calls.

Hughes, a GSA employee who used to fly planes just as the late Hughes did, says "I thought this would start to die out now that old Howard Hughes was gone." But the jokes continue, and he can't resist recounting one. When he boarded a commercial flight from Cincinnati to Chicago - "It was in the middle of the night; I was taking advantage of the night rates" - there was much laughter among the flight crew ("Guess who's on board tonight?"). As for Hughes, he experienced the unstinting attention that the more famous Hughes might have received.

On the big DC-8 bound for Chicago that night, Howard Hughes was the only passenger.