The formal court proceeding in felony cases where the defendant is officially notified of the charges and asked to enter a plea is called a/an:

Plea bargain

Explanation:This is where someone knows what they are facing and having been told their charges they can make a plea bargain which may be to say I will plea guilty in order to have the sentenced reduced by this years.

Plea bargain mostly opens up for the defendant to take up the punishment if the they plea guilty at a much lesser cost than it would have been if they didn't plea.

The court appearance where the defendant enters a plea and the case is set for trial is called an arraignment