RELAXING AT a restaurant table, you sip your drink by candlelight and chat with your companion, appetite slowly building. The waiter brings the menu. With anticipation you begin to scan the seafood entrees: broiled ratfish, fried grunt, poached mudblower with parsley sauce.

Ratfish? Mudblower? How disgusting. Maybe you don't want seafood after all. What else have they got?

This is the kind of reaction that frustrates the National Marine Fisheries Service. If only people knew. If only they realized how great ratfish tastes. If only they would try ratfish. If only ratfish had a different name.

Why yes, a different name. Butterfly fish, perhaps. Or sunshine fish. Honey fish.

The National Marine Fisheries Service is renaming fish. It has launched an ambitious program, involving more than 50 persons so far, to solve a problem acutely exasperating to those who manage our marine resources: While familiar kinds of food fish dwindle in population, dozens of delicious and nutritious species contentedly swim and jump, increase and multiply, protected by repugnant names. Living is easy when your name is toadfish.

The Fisheries Service has not, however, simply replaced the offending names. Rather, as a bureaucratic agency in good standing, it began some years ago to study the problem. Soon it discovered complexities. The red-ear fish, for instance, is also called the stumpknocker and the roach.

Moreover, new fish names might be unfair. How would a viperfish fisherman feel if lizardfish, which his competitor fishes for, got a prettier name?

In any case, is it certain that people want the names changed? It is always possible that they have come to like names like croaker, hogsucker and hunchback scorpionfish.

So, late in 1973, the agency filed a public notice, asking the eating public for comment. Five hundred eaters responded. The Fisheries Service tallied the responses and reached a bureaucratic conclusion: "A need exists for the clarification and refinement of policies and procedures that govern the nomenclature of fish and fishery products for purposes of marketing and labeling of these products."

Now fish could get new names, right? Well, not yet. The Fisheries Service wasn't exactly sure how to go about solving the problem. Therefore, says one of its officials, James Brooker, "we decided to engage some expertise to make a proposal of how we could go about solving the problem."

A feasibility study was decided upon. Bids were sought. In 1974, the Fisheries Service awarded a $63,000 contract to a Chicago consulting company called Brand Group Inc. to study feasibility.

Brand Group found it feasible to rename fish. The company did not, however, actually rename any. First, it said, an "organization framework" was needed. To obtain that, the Fisheries Service engaged Brand Group to do a second study. This study would develop a "prototype model identification system." Its goal: "to identify and prioritize a set of factors to be used in comparing and organizing the species."

Brand Group began to develop a prototype model identificatin system. In the sea, ratfish continued to multiply, uneaten.

The prototype model identification system, it must be acknowledged, did not produce any new fish names either. What did produce was a series of "edibility profiles." Fish were rated, on scales of 1 to 5, for flavor, fattiness, odor, color, flakiness, firmness, coarseness and moistness.

Unfortunately, this did not simplify the renaming of fish. The fish did not fit neatly into edibility groups. In fact, a total of 390,000 different fish edibility profiles were possible.

Again the Fisheries Service asked the nation's fish eaters for advice. But they only complicated matters further. "I would like to know where a fish was caught, and by whom," wrote one citizen. A Florida man said the system should make clear "which of the eight edibility factors indicates whether ratfish tastes similar to tuna."

The agency vigorously rejected a third correspondent's advice: "About fish -- leave it alone."

Frustrated, the Fisheries Service decided to call in the Army. It turned to the U.S. Army food research laboratories in Natick, Mass. The Army was not asked to suggest new fish names, however. Instead, it was told "to develop objective methods of measuring edibility and to determine the validity of the proposed eight edibility factors."

The Army, its mission assigned, referred the matter to a "flavor panel" and a "texture panel." It hasn't published any conclusions so far. When last checked, employes of the Army food research laboratory were eating fish.

To be on the safe side, the Fisheries Service asked Brand Group Inc. to do a third study. This one aims to produce a "uniform nomenclature" for fish forms, such as fillets, and fish modifiers, such as mustard sauce.

As for the Fisheries Service itself, it remains as concerned as ever about the sorry names some fish have. The service has so far spent seven years and $494,000 trying to find new names for them. It hasn't found any yet, but it is confident that it will.

Hogsuckers aside, many are pleased with this prospect. "The industry is enthusiastic," says Steven Pokress, head of the unit of General Host Corp. that markets frozen fish. "It will open up the market to a lot of species that have been ignored because their names are a turn-off."

However, there is one last bureaucratic hurdle the National Marine Fisheries Service must leap before it can bestow mouthwatering names on the lizardfish, the roach, the grunt and the croaker: The Food and Drug Adminstration says it alone is in charge of the names of fish.