Convening for the first time in 2011, the New Jersey Supreme Court heard arguments Tuesday on whether the rules on naming of law firms should be relaxed in recognition of modern modes of professional practice and identification.

The Alpha Center for Divorce Mediation, which operates seven offices in New Jersey, has appealed a court committee’s finding that its name violates Rule of Professional Conduct 7.5, which says law firms, except for nonprofit legal services agencies, must be named after the lawyers who run them.