Do I say my name or run out of the room?

So you are sitting in a circle in school or at a business meeting, the teacher/presenter says, "Let's go around the room and introduce ourselves". Most stutterers want to hide. How many of us can't say our name in this situation? I was the expert on going to the bathroom during this time, having to make a phone call or faking a coughing spell. Anything and I mean anything to get out of the room. Sometimes it worked and they skipped me, but I usually felt deep shame inside. I felt invisible. So what are my options now.? The first is to continue to remain invisible. The second is to voluntary stutter and let the cat out of the bag, ex: my my my name is Lori. The third is to try and breathe and use my tools. I would choose # 3 first and then revert to #2 if I really panicked. I would recommend to conquer the fear. It gets easier. Ask yourself, if I stutter, what would happen? Would anyone really care? If you said, bear with me I stutter sometimes and then said your name, wouldn't most people be understanding? Is it worse to face the fear head on or escape? This is why it is soooo important to practice your tools when your don't need it, so you have it under stressful times.