The big slogan button that Soviet Ambassador Anatoliy F. Dobrynin was sporting on his suit lapel proclaimed, "First Dog" in blue jean letters.

"It came from an American friend because I am dean of the diplomatic corps in Washington," Dobrynin explained at an inaugural brunch for 400 given at the Organization of American States in honor of the diplomatic corps.

Obviously, the American friend was not Secretary of State Edmund S. Muskie, who had summoned the Russian ambassador to the State Department on Saturday to complain strongly about "scurrilous propaganda" in Soviet press commentary on the Iranian hostage negotiations.

Gen. Alexander Haig, soon to be Muskie's successor, was expected at the brunch but did not appear and so missed meeting a smiling and genial Dobrynin, who moved about chatting with his fellow diplomats and was among the last to leave the reception. When Maureen Reagan came to his table, the Soviet ambassador embraced the president-elect's daughter and kissed her on the cheek.

The brunch was staged by Donald M. Kendall, chairman of PepsiCo, a Republican supporter and fund-raiser prominent from the Nixon years. In the great cola wars, Pepsi won the right to the Soviet market under Nixon while rival Coca-Cola gained the Chinese market when Georgian Jimmy Carter was in the White House.

Attending the Pepsi-sponsored brunch, the ambassador from the People's Republic of China wasn't going to be caught in an undiplomatic commercial for either soft-drink product.

"He says he can't tell the difference," an interpreter explained when Ambassador Chai Zemin was asked about the cola franchise in his country.

Most of the 150 members of the diplomatic corps and their wives turned out for the Reagan inaugural brunch. Among them was Ramon Sanchez-Parodi, counselor of the Cuban interests Section, which represents the Castro regime here.

The Pepsi party drew several Reagan Cabinet officers-designees, including incoming defense secretary Caspar W. Weinberger and transportation secretary-to-be Drew Lewis. The guests brunched on baked salmon and chicken-mushroom crepes in the elegant, three-chandeliered drawing room of the OAS.

Vice President-elect George Bush stopped by to offer the Reagan administration's greetings to the foreign diplomats.

"We are going to make your job a lot easier . . . with a foreign policy that has stability and direction," he told the diplomats, emphasizing that world affairs will receive "paramount" interest from the new administration along with emphasis on the economy.