The Better Business Bureau of Metropolitan Washington has named Suburban Bank Executive Vice President Warren P. Rothe as its 1983-'84 chairman and Woodward & Lothrop Executive Vice President Arthur J. Pugh as its vice chairman.

Rothe and Pugh were elected by the Better Business Bureau's 39-member board of directors, who represent about 4,000 bureau members in the metropolitan area.

Rothe heads the corporate banking group of Suburban Bank. He is responsible for commercial loans and business development programs and services. He joined Suburban in 1953 while a high school student. He was named assistant treasurer in 1964, became a vice president of the bank in 1972 and was named to his present position in 1980.

He also is president of the Montgomery County Economic and Business Development Corp., a firm maintained by the county government and local business to offer long-term, low-interest financing to small businesses.

Pugh joined Woodward & Lothrop in 1960 as a management trainee. He was manager and director of several area stores before being named vice president of operations and customer services in 1971. In 1977, he was promoted to senior vice president of operations and took on his present position of executive vice president of operations in 1980.

He is a vice chairman of the operations division of the National Retail Merchants Association and a member of its board of directors. He is also a member of the Metropolitan Board of Trade.

The Better Business Bureau of Metropolitan Washington was founded in 1920 to act as an intermediary between consumers and local businesses. Last year, the trade group received about 100,000 inquiries and processed 8,168 complaints--5,061 of which President Douglas W. Tindal said were closed to the customer's satisfaction. The bureau is supported by its 4,000 member firms, each of whom pays an annual fee based upon the number of people they employ.