William B. Snyder, executive vice president of the Government Employees Insurance Co., was selected as the firm's president yesterday.

Snyder, 50, joined Geico in April 1977 as senior vice president and a year later assumed responsibility for marketing and field operations. Snyder served as executive vice president since last May.

John J. Byrne, Geico chairman of the board, will remain as chairman and chief executive officer of Geico and chairman, president and chief executive officer of Geico Corp., the holding company for the insurance company.

In addition to Snyder's election by the Geico board of directors, Byrne said that the company has declared a quarterly cash dividend of 10 cents a share on the outstanding shares of common stock payable on March 31 to shareholders of record March 10.

The corporation also has purchased since the second quarter last year 1,480,998 common share equivalents of its own stock of the 1.5 million shares previously authorized. The corporation's board of directors has authorized the purchase of 1.5 million more corporation common share equivalents "from time to time," the company said.

Before joining Geigo, Snyder was vice president for marketing at Travelers Corp. where he was responsible for management of sales and support functions for life insurance, health insurance and financial services.

Geico is based in the Washington area and is recovering from financial difficulties which almost resulted in its bankruptcy about four years ago.