Bentley Coffey (Clemson University, Department of Economics) & Patrick McLaughlin (George Mason University, Mercatus Center) have published From Lawyer to Judge: Advancement, Sex, and Name-Calling, 11 Am. L. & Econ. Rev. 112 (2009).  Here is the abstract:

This paper provides the first empirical test of the Portia Hypothesis: females with masculine monikers are more successful in legal careers. Utilizing South Carolina microdata, we look for correlation between an individual's advancement to a judgeship and his/her name's masculinity, which we construct from the joint empirical distribution of names and gender in the state's entire population of registered voters. We find robust evidence that nominally masculine females are favored over other females. Hence, our results support the Portia Hypothesis.

The ABA Journal reports on the article in Female Lawyers with Masculine Names May Have a Better Shot at Judgeships, by Debra Cassens Weiss:

Women lawyers with masculine-sounding first names have better odds of becoming a judge than their counterparts with feminine names, at least in South Carolina, according to a study by two economics researchers.

The study finds that changing a woman’s name from something feminine, such as Sue, to a gender-ambiguous name such as Kelly, increased the odds of becoming a South Carolina judge by about 5%, the Vancouver Sun reports. Changing the name Sue to a predominantly male name such as Cameron tripled the odds of becoming a judge, and changing it to Bruce increased the odds by a factor of five.

The researchers suggest the reason for the odds may be the “Portia hypothesis,” named for the Shakespeare character who disguises herself as a man to argue a court case, according to excerpts of the study posted by the Situationist. The theory holds that those females with male-sounding names are more successful in legal careers than females with feminine-sounding names. …

Coffey told the Sun that he and his wife, a lawyer, were so swayed by the study findings that they named their daughter Collins.

Legal Blog Watch notes that the theory does not hold true for the U.S. Supreme Court, as Justices O'Connor (Sandra), Ginsburg (Ruth) and Sotomayor (Sonia) all have feminine-sounding names.

The theory also does not fit the U.S. Tax Court, as Judges Cohen (Mary Ann), Kroupa (Diane), Marvel (Paige), and Paris (Elizabeth) all have feminine-sounding names, as does Senior Judge Chiechi (Carolyn).