Nine persons have been recommended to President Reagan for consideration in filling three vacancies in District of Columbia courts.

The D.C. Judicial Nomination Commission recently selected the candidates for two vacancies on the Superior Court and one on the D.C. Court of Appeals.

Wiley A. Branton, chairman of the commission, said the names of three candidates have been submitted for the Superior Court vacancy created by the retirement of Associate Judge Luke C. Moore: Arthur L. Burnett Sr., 52, U.S. magistrate for the U.S. District Court for D.C.; Joel M. Finkelstein, 48, a partner with the law firm of Margolius, Davis, Finkelstein & Rider, and Leroy Nesbitt, 53, a private practitioner.

For the Superior Court vacancy created by the retirement of Associate Judge Donald S. Smith, the names are: William L. Davis, 53, deputy D.C. corporation counsel for the Criminal Division; Cheryl M. Long, 38, director of the Public Defender Service; and Mildred M. Matesich, 39, who recently resigned as chief staff counsel for the U.S. Court of Appeals for the D.C. circuit.

For the vacancy on the D.C. Court of Appeals created by the retirement of Associate Judge Frank Q. Nebeker, the names are: Frederick B. Abramson, 52, partner in the law firm of Sachs, Greenebaum & Tayler; Clarice R. Feldman, 45, a private practitioner, and Superior Court Associate Judge Frank E. Schwelb.

The president has 60 days from receipt of the commission's recommendations in which to nominate a person for each judicial vacancy. Senate confirmation is required.