I've been an ice monitor for three reluctant years. Here's how we do it:
You sign up with the monitor at the beginning of the session. The monitor signs you up because some coaches will sign up a skater four or five times using variations of the skaters name. Ex: Cassandra: Cassie, Cass, Sandi, Sandra, CJ Lastname, etc. Sneaky, eh?
When I play the music, if I'm handed a cd with no name, I hand it back immediately and say "I can't play this. Find a sharpie and get back to me. I'll hold your spot." I call out the name twice. No response, I go on. Since I also skate the session, waiting around wastes my time and my time is valuable.
Once your program is played, your name is crossed off. If you skipped and want it played later, after everyone goes once, you go. However, your spot has been changed and you are now at the end of the list.
That's how I do it. Good luck. It's a thankless job.