Fannie Mae is her name and "chicken" is the game being played in Washington about her future.

At least that's the view of Wall Street analyst Elliott Schneider, as he literally explodes about the warfare in progress over an institution called Federal National Mortgage Association.

That cumbersome title alone puts average Americans to sleep and helps explain why you don't hear anything on radio or television about the pitched battles and guerrilla warfare all over this town. But Washington bureaucrats long ago reduced that long name to the acronym of FNMA, the pronunciation of which has gone down on legal record books as Fannie Mae.

All these terms tend to obscure the significant role played in America's economy by the company, today the largest single provider of funds for the nation's housing market and owner of mortgages with a total value exceeding $33 billion.

Fannie Mae also is a profitable business venture, earning $165 million in 1977 ($3.15 a share) compared with $127 million ($2.62) the previous year.

A war over Fannie Mae has been growing in intensity since the early days of the Carter administration, when the Department of Housing and Urban Development joined with some Democrats on Capitol Hill to seek new FNMA leadership - managers who they said should direct FNMA attention and resources to the problems of housing in the country's cities.

Proposed legislation in the Senate last year, to effectively "pack" FNMA's board of directors with more government appointees, failed to muster adequate Banking Committee support.

HUD, meantime, raised more questions than had been traditional about Fannie Mae mortgage programs before giving final approval. In some instances, the needed approval was delayed for long periods as HUD sought to emphasize its new determination that lower-income and moderate-income housing required more FNMA support.

FNMA management was asked to supply details on future activities as screws of federal government regulation began to tighten, representing vague authority always in the hands of HUD but never applied previously under Republican administrations.

Board meetings became acrimonious, with appointees of President Carter voting against management and seeking, at times, to condemn top officers and fellow directors. HUD asked the White House to remove management directors at FNMA "for good cause," as permitted by FNMA's government charter. And HUD began to withhold blanket approval for longterm mortgage buying commitment of Fannie Mae.

In February, all these events culminated in about 50 hours of extreme bitterness as Fannie Mae's management again prevailed over the Carter board members in approving a new slate of directors for stockholder approval. HUD retaliated two days later at a briefing for reporters, when proposed new rules to regulate Fannie Mae were made public.

"Rape of Fannie Mae?" was the headline for an editorial in Barron's magazine, the next weekend, arguing that for HUD to move "in on Fannie Mae . . . strikes us as tantamount to the inmates running the asylum."

Schneider, who works for the firm of Gruntal & Co., is not so willing to put all the blame for what is happening on HUD or its plain-speaking chief executive, Secretary Patricia Roberts Harris.

He has concluded that Fannie Mae Chairman Allan Oakley Hunter staged "the wrong fight at the wrong time" in the recent confrontation over three new board members, for example. One anti-Hunter man lost his seat and Hunter gave up positions on the board of two company executives, in what was described as a gesture for peace with HUD. But the persons selected all had some ties to FNMA or its directors and officials, and the action only angered HUD.

Schneider's interest in Fannie is that of an investor, a stock market analyst and an economist. Over the years, he has been sharply critical of FNMA's management and always concerned about Big Government's potential involvement in Fannie's affairs.

Not content to be a voyeur, Schneider takes an active role as a stockholder of Fannie Mae and outside watchdog, firing off letters of criticism to presidents. Cabinet secretaries and Fannie Mae's leadership. He speaks loudly at annual meetings and his fellow stockholders listen.

He also publishes regular research on the company, a recent copy of which included his assessment of today's "chicken" war over FNMA. He said:

"In many ways it is like the game . . . sometimes played by disturbed teenagers, in which one party drives his car directly at that of another party where the loser, the chicken, swerves away first.

"Another and potentially more destructive version of the game occurs when one person plays the game with whoever happens to come along on an open road."

It is this last version that Schneider says Secretary Harris has started to play with Fannie Mae. "Her vehicle is her control over the company's ability to borrow," he stated.

There is no controversy about whether HUD has such controls but, in the wake of recent developments in a growing battle over the stewardship of Fannie Mae, serious questions have been raised in the financial markets about the general impact of the strategy being used by HUD to demonstrate its might.

To cite just one example, HUD has been withholding until virtually the last moment authority for Fannie Mae to make commitments on buying future mortgages at its regular auctions, held every two weeks. Although HUD official s dismiss the possibility, financial industry experts contend that the government department's action has created enough uncertainty to drive up interest rates in recent weeks.

With the jump in interest rates, Fannie Mae has been deluged with demands from builders and mortgage bankers for commitments to buy home mortgages at future dates. And if interest rates remain at higher levels, those commitments will become real mortgages in Fannie Mae's future portfolio.

Last week, HUD boosted to 8 3/4 percent from 8 1/2 percent the legal limit on interest rates for FHA mortgages in general recognition of rising money costs. But some mortgage bankers described the quarter-percent boost as not realistic and said one-helf percent would reflect today's mortgage market more accurately (with average D.C. area rates now 1/4 percent and higher, for example).

Schneider, for one, said last week that had HUD increased the rate to 9 percent, it might have been seen as an admission that its warfare with Fannie Mae has contributed to rising rates.

John C. Opperman, president of the Mortgage Bankers Association of America, says that, without long-term authority for FNMA to buy mortgages, the alternative is higher interest rates and disruption of the entire residential mortgage market.

"Uncertainly over the continued availability of commitment authority cannot help but further erode the market . . . unprecedented volume (of recent demand for FNMA's mortgage commitments) reflects an increasing concern on the part of lenders that further deterioration lies ahead. It is precisely at times like this that the housing industry needs FNMA's most active support," he wrote Secretary Harris a month ago.

Indeed, with mortgage sellers nervous, February was a record month at FNMA. Some $2 billion of commitments to buy mortgages in future months were sought by sellers, an annual rate of $24 billion. If interest rates turn downward, perhaps only half the commitments will be delivered as real mortgages. But there is no doubt about mortgage market nervousness.

Thus, the timing of the current warfare couldn't be worse. A collision course appears inevitable with Fannie Mae promising a court challenge to HUD's new rules if the regulations are made permanent after a 30-day period for public comment.

Litigation would cost money, sapping resources of both the federal government and a company with a public purpose. Years could pass before a final decision.

At its heart, the battle for Fannie Mae may simply reflect basic philosophic differences that have haunted the company from its beginnings as a government agency in the Depression years.

Initially, Fannie Mae was patterned after the central banking system and designed to be a cooperative owned by its users, the mortgage banking industry. But the concept didn't work because of the absence of major capital resources in mortgage banking. It became a government agency, charged with support of the so-called secondary mortgage market, buying up mortgages in periods of tight money to free more funds for other mortgage investment and selling mortgages when credit was easier.

When the administration of President Lyndon Johnson decided to remove fannie Mae from the government budget and set it up as a private corporation, officers at HUD objected because they saw the agency as a vital tool in federal housing policy. But the HUD people lost and Fannie Mae became a private firm as the 1970s began.

Today, FNMA is listed on the New York Stock Exchange and its stock is one of the most actively traded nationwide issues.