Cellular Radio Corp., a mobile phone system distributor and developer based in Vienna, has named James B. Graham president and chief operating officer.

Graham, 31, joins Cellular Radio after 10 years with Western Union Corp., where he was executive product manager for priority mail products.

A native of Washington who received both his undergraduate and graduate business education at Virginia Polytechnic Institute, Graham also is a former director of finance and administration for the Carnegie Endowment in Washington.

He succeeds James C. Davis, who resigned because of poor health. Davis will remain a consultant and a member of the company's board.

Graham said in an interview that he would like the company to become the nation's chief supplier of cellular phone switching equipment. The industry will be growing extremely quickly, he said, as new cities adopt mobile phone service and the new technology is able to cover greater distances.

The number of cities with cellular phone markets will double to 60 by next year, Graham predicted.

Helping Cellular Radio compete in the high-stakes industry is Andrew H. Lamothe, who heads the firm's technical staff, Graham said.

Lamothe was employed by Motorola as a design engineer from 1971 to 1979, and by American Radio Telephone Service Inc. as director of engineering from 1979 to 1983. He helped the latter firm develop and install the Cellular One system in Washington.

The 1 1/2-year-old, privately held firm, which has offices in Dallas and Miami in addition to its Tysons Corner headquarters, develops the software for mobile phone operating companies such as Cellular One and Bell Atlantic Mobile Systems in Washington. It also distributes mobile phone equipment and does consulting work.