A federal judge overseeing a bitter trademark dispute over the late Johnnie Cochran Jr.’s name is preparing to decide whether The Cochran Firm is a national law firm or a network of partnerships.

The firm’s business structure came into question after Randy McMurray, who ran the Los Angeles office between 2007 and 2012, alleged in a lawsuit that the firm is misleading the public about how it operates. His claims are part of his effort to lift an injunction barring him from using the Cochran name when advertising legal services. The Cochran Firm filed the trademark infringement lawsuit against McMurray after he began operating as The Cochran Law Group.