Among local attorneys, there's a name for the Reagan administration's proposed overhaul of the immigration system: the Lawyers' Relief Act of 1981.

Veteran immigration lawyers and government officials said last week the plan to control immigration overflow and to legalize 6 million people already in this country illegally -- including 50,000 or more in the D.C. area -- would mean a bonanza for immigration lawyers, already working at capacity because of the system's complexity.

If the overhaul passes, said immigration lawyer Michael Maggio, "it will make what is already the most overworked, under funded and disorganized bureaucracy in the government [the Immigration and Naturalization Service] even worse."

Any overhaul of such a complex set of laws will create legal problems and legal questions, immigration lawyers pointed out. That makes the program, one lawyer said, a "dream package" for lawyers.

But it also makes it misery for the aliens, Maggio said.

The administration's plan would allow the estimated 6 million illegal alients in this country to apply for permanent residency and eventual citizenship if they entered the country before Jan. 1, 1980.

Aliens applying for the program would have to show proof that they were here before then. That will lead to a virtual assembly line of phony documents, predicted one knowledgeable state department official who asked not to be identified.

That official also predicted that few aliens will come forward because they distrust government in general and fear the INS in particular.

Many will be afraid that if tyhey came forward, they would be determined ineligible to stay here, he said, some because they re-entered after once being departed, or committed a crime back home, or are on welfare here.

Under present law, aliens who are "likely at any time to become public charges," he said, are excludable. It does not appear that the new proposal will change such provisions.

"And people who do come forward will want their lawyers in front of them to make sure everything's okay," he said. "People refuse to go alone to INS even when the legal paperwork has been done for them. They are scared to death."

Complex and contradictory regulations and myriad and confusing forms, especially for people who don't speak English, force many alients to hire lawyers. It's so complicated, Maggio said, that two lawyers who wanted to hire a foreign domestic as a housekeeper failed twice and had to hire an immigration lawyer to help them.

Sometimes even that's not good enough, said immigration lawyer Jan Peterson. "I tried to sponsor [a foreign worker] as a domestic myself and lost."