In law school, it’s common for students to be taught to give a somewhat grand introduction at the beginning of their moot court arguments. “MAY IT PLEASE THE COURT!”, the student is taught to announce, very slowly and formally, followed by an extended introduction that usually goes something like this:
“My name is Joe Student. I am here with my co-counsel, Jane Student. Together, we represent the Petitioner, James P. Robinson, in the case before you today. We will be dividing our argument. I will be arguing first, and I will discuss the First Amendment issues. Next, my co-counsel will argue second, and she will discuss the Due Process issues.”
Then the actual presentation begins. (See, for example, here at the 3:15 mark)
My sense is that this very formal presentation is pretty rare outside moot courts, though. In real life, it’s much more informal. In most courts, the judges have probably been hearing argument all day or even all week, and they’ve called your case and called you by name. They just need you to say for the appellate record who you are. In the usual case of an undivided argument, the whole introduction might just be a brief, “May it please the court, Joe Student for Mr. Robinson,” followed by the argument. Part of the reason for the informality is time, too: If you only have 15 minutes, even just a 30-second introduction is cutting into your precious time.
Of course, if you’re a student in moot court and you are specifically instructed to make a formal introduction, then do it. But I thought it might be worth noting that it’s usually less formal in practice.