The American embassy in Taiwan may be renamed the Asian-American Services Corp., while the Republic of China embassy in Washington may be known as the Sun Yat-sen Center.

But Carter administration officials said yesterday they expect cultural and trade relations with Taiwan to contine to grow despite President Carter's decision to establish diplomatic relations with Peking and sever all military and diplomatic ties with Taiwan.

The key mechanism in the new arrangement between Taipei and Washington will be a private corporation empowered through Congress to conduct business on Taiwan, including such duties as issuing travel documents, U.S. officials said yesterday.

"There's a lot of mechanics to go through, but it can be done," Herbert Hansell, the State Department's chief legal officer, said of the overhaul. "After all the papers are shuffled, we will contined to conduct - on a non-official basis - a whole spectrum of relations with Taiwan."

The new corporation would be patterned after the association Japan set up on Taiwan after breaking off

Formal relations in 1972, "It just so happens the head of the association is a 'retired' Japanese ambassador," an official said.

The administration also will have togo to congress to make changes in several laws to include Taiwan in therequired definition of a "Country" for future dealings with the United States, officials noted.

The Export-Import Bank, Overseas Private Investment Corp., "most favored nation" trading clause, and arms transfers laws are among items needing alteration, they said.

Officials stressed that the administration is anxious to preserve bomming U.S. Taiwan trade, which reached $5.4 billion in 1977 and is projected at $7.4 billion this year. Of that total, $2.3 billion is U.S. exports, leaving a deficit of $2.8 billion.

By comparison, U.S. trade with the People's Republic of China was only about $374 million last year, and, though growing rapidly, just under $700 million for the first nine months of this year.

In addition, American business has more than $500 million invested in Taiwan and Ex-Im Bank guarantees totalled $1.7 billion as of last month, according to State Department figures.

Specifies on the technicialities of the new relationship were still sketchy in many instances yesterday. "We're missing precedents," one State Department official said. "But that's somewhat fortunate because it gives us a wide ranges of choices."

Frank Tao, spokesman for the Republic of China embassy, said yesterday it was "too early" to answer questions about the future of his embassy here.

But Taiwan has plenty of experience in dealing with countries where it no longer has formal diplomatic ties.

For instance, when Spain recognized Peking and broke relations with Taiwan in 1973, the number two man in the Nationalist Chinese embassy stayed on to run the Sun Yet-sen Center in Madrid and a Spanish counterpart in Taipei became head of the local Cervantes Center.

Foreign visitors from such countries travel to Taiwan with "letters of recommendation" rather than visas and find a separate window at Taipei International Airport to serve them.

Like the Japanese Interchange Association in Taipei, the new American presence will require that U.S. diplomats be detached from their officials Foreign Sevice roles. "It's kind of like guys who 'retire' from the CIA," a congressional expert said.

Officials said the corporation probably will be chartered under District of Columbia corporation laws, as were the Legal Services Corp. and Amtrak, after congressional approval.

Opposition is not expected from conservative members of Congress outraged at the president's announcement, because the legal gymnastics will help Taiwan, according to officials in the administration and on Capitol Hill.

An effort might be made to increase military sales to Taiwan when the necessary "semantic tinkering" on the arms transfer laws is forwarded to Capitol Hill, according to one congressional aide. But it is not likely the conservatives have the votes to pass such a measure, much less override a veto, he said.

Other U.S.-Taiwan treaties governing a variety of issues - from air landing rights to postal service and movement of nuclear materials - also are expected to be continued, officials said.

Stanford University professor Victor H.Li, author of a study on the legal problems of "de-recognizing" Taiwan, said yesterday in a phone interview from Taipei that he agreed with the administration that its formula for continuing "unofficial" relations could be achieved.

"You have to play with words, but it can be done," he said. "That's why I'm sure there were a lot of intended ambiguities in the comminique with peking."

Li and other China experts were less certain about the impact of Carter's decision on internal politics in Taiwan. Li noted that residents in the Taiwan capital were curious about the timing of the announcement. It came just before scheduled elections - now postponed.

"There obviously have been a lot of unspoken signals between Washington and Peking," another scholar said. "We don't trumpet the continued arms sales. They don't make noises about invading Taiwan. Certain activities will just go on unsaid."

Although future U.S.-Taiwan ties may also have to be unspoken and unofficial, administration official, administration officials were making clear yesterday that the connection will remain.