Christian Badea was named yesterday to the post of Exxon/Arts Endowment Conductor of the National Symphony Orchestra.

Born in Romania, Badea, who is 30, is a permanent resident of the United States and a 1976 graduate of the Julliard School in New York City. Last spring he auditioned for Mstislav Rostropovich, the NSO's music director, who selected him out of a number of conductors who were hoping for the Washington assignment.

The conductor, who is unmarried, already has a Washington apartment and will be moving here shortly. He is also music director of the Savannah, Ga., Symphony, a post he will retain while working with the National Symphony.

Badea's appointment follows the recent resignation of Murry Sidlin, who left the Exxon/Arts Endowment post with the National Symphony to become music director of the New Haven, Conn., Symphony. The Exxon/Arts Endowment program, which is funded by both the oil company and the National Endowment for the Arts, assists young conductors to prepare themselves for major conducting assignments.

Badea has guest-conducted the National Orchestra of Belgium, one of the Juilliard orchestras, the New York City Ballet, and opera at the 1977 Spoleto Festival in Italy. He has studied with Herbert von Karajan, Rene Defossez, and Sixten Ehrling, and has recorded the Beethoven Eighth Symphony with the BBC Symphonyof London.