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Everyone started out as a new mystery shopper at some point and we all make mistakes. I'm sure even some veterans would say they are still learning. You just have to learn from the mistakes.
For me, identifying a manager is easy. It's usually someone who is active in the restaurant, visiting tables, leading employees, someone who dresses differently than the servers. It could be one or any of those things.
For reporting purposes, an assistant mgr and a manager are the same to me.
Some MSC want you to identify and get a manager's name, some may only want you to observe and report on them, some don't need any info.
If you need to get a name, for your situation, you could've said, "You've been very helpful or nice, what do you do here and what is your name ?" If it's a fine restaurant, you could ask the server for the managers name because you are thinking of having an event and want to be able to speak to the manager. Be creative and make sure it fits the scenario/environment you are in.