WASHINGTON, Oct 12-The Supreme Court today named former Solicitor General Archibald Cox, Williston Professor of Law, to serve as attorney for Edward H. Coolidge Jr., who was convicted of murdering a New Hampshire girl.

The Court agreed earlier this year to review the 1964 case because of questions Coolidge raised about a search for evidence in the murder of 14-year-old Pamela Mason of Manchester, N.H. Coolidge was sentenced to life imprisonment.