Jimmy had that plan to screw Chuck from the second he walked into that office. He already knew he wasn't getting an insurance refund. By not having his policy number, he exposed Chuck as being his brother, then the agent was able to put two and two together during his "breakdown".
By not having his policy number, he exposed Chuck as being his brother
he never had the policy number
The kicker was he just gave his last name. He knew Chuck would come up first on the computer list and that Chuck's name would be recognized by the agent. An attorney would usually give his full name when asked, even Jimmy just goes by "Jimmy" to his clients, he doesn't usually use just his last name McGill.