Again, the purpose here is not to identify specific companies. It's to open a discussion that will reveal the names of people who can offer even more help. The secondary purpose is to get the coach to talk. The more he talks, the more you learn. Tell me more about how you fit into this industry of ours, and what you do.
People love to talk about themselves and their work.
This applies to your coach, too. When you reveal interest in the coach, you open the information gates. The only interruption you should make is to ask for amplification about specific companies and people, and for advice. You know a lot of managers in this industry. If you want to talk about your abilities, and to find out where you might fit among the people and companies your coach knows, give your coach the chance to make the connections for you.