Investors placing bets on commercial lawsuits have long operated under a veil of secrecy. But as litigation funding in the U.S. has spread to more courthouses and transformed into a billion-dollar business, plaintiffs and their faceless financiers are confronting calls for more transparency.

At the urging of the U.S. Chamber of Commerce, the arm of the federal judiciary that oversees procedural rules recently decided to examine whether the court system should require all civil litigants to reveal financing deals with outsiders...