Last month, five seafood restaurants in San Diego attached "edibility profiles" to their menus so customers could get a better idea of what shark and local fish such as Corbina and Sculpin taste like.

For the National Marine Fisheries Service, that was the first step in an effort to change the fish-eating habits of Americans. If enough restaurants and markets adopt the profiles, the fisheries service thinks it may have found a way to solve a little-known national dilemma it calls the "fish nomenclature problem."

That, put simply, is the problem caused by the fact that few Americans will eat things called ratfish, or mudblowers, or pigfish, or monkfish, or cancer crab or spiny ghostsharks. All of those horrid-sounding fish are edible and nutritious, the fisheries service contends.

"People think this is all a joke," explained James R. Brooker, a seafood research expert at the fisheries service. "Some of the fish names are funny, but this is a real problem."

The government discovered the problem in the early 1970s when the fishing industry complained that the stocks of popular fish, such as Arctic cod, haddock, flounder and herring, were dwindling. The industry said the demand for those species could be reduced if consumers would begin eating "under-utilized" species, many of which are unmolested by fishermen simply because they have distasteful names.

The industry's solution was simple. It asked the government to rename certain fish.

So in 1974, the fisheries service awarded a $63,000 contract that turned out to be the first step in development of the edibility profile. A Chicago consulting company, Brand Group Inc., was asked if the nomenclature problem was real. Yes indeed, said Brand Group after a year's work, but that's just the beginning.

Some canneries list all 16 species of anchovies as "sardines," but others consider only a few species as sardines. Consumers had no way of knowing what they were getting, which could explain why two tins of sardines packaged by the same company could taste differently, Brand Group said.

Companies also used several names to market the same fish, Brand Group said. A species known scientifically as Sebastes Marinus was commonly called rosefish or redfish until it was marketed in the Midwest, where it became ocean perch, even though there are no perch in the ocean.

Government regulations have contributed to the confusion. The Food and Drug Administration requires that fish be identified by their most common names. Thus, the same fish is known in New England as the redfish, but in Portland, Ore., as the yellowfish. Some fish are known by as many as 25 names.

Brand Group advised against requiring companies to identify fish by their scientific names (which most consumers probably would not recognize) or renaming fish, because both steps would probably add to the confusion.

What the government really needed to do, Brand Group said, was to forget about names and concentrate on a more meaningful way to describe fish to consumers.

It suggested the eight-factor edibility profile, which would rate fish on a scale of 1 to 5 for flavor, fat, odor raw, color cooked, flakiness, firmness, coarseness, and moisture cooked.

The fisheries service called out the Army for help with the idea. Twenty experts at the Army's food research laboratory in Natick, Mass., began searching for a scientific way to measure the eight edibility factors. In 1980, the Army released a 630-page report outlining its methods and the edibility profiles of 17 fish.

After six years of research and nearly $500,000, the fisheries service had found a way to "scientifically judge fish" without using their names, said Brooker, who added that the United Nations has shown interest in adopting the profiles worldwide.

"Our customers really like it," said Craig Ghio, co-owner of the San Diego-based restaurant chain that began using the profiles. "They often want to try something new but they don't want to get something they won't like. The profiles give them a chance to see that shark, for instance, is a mild, dry fish that has a lot of the same taste qualities as halibut," Ghio said.

The fisheries service has completed 12 more edibility profiles since 1980, Brooker said, and is in the process of hiring a marketing firm to suggest ways to introduce the public to the profiles.

That doesn't mean, however, that the government has abandoned the suggestion that it change a few ugly fish names. "There would be some problems doing it," Brooker said, "but they wouldn't be insurmountable."

That's still being studied, Brooker explained, because the government is convinced that an elephant fish really would taste better if it had a prettier name.