"I might have been mistaken for a different person." is correct. It can be used when you think someone is a certain person, but it turns out that you were wrong. This is mistaking someone for a different person. "Misunderstood" would be used more in situations where you don't understand what someone is saying, for example. "I may have misunderstood what she was saying." Hope this helped!! :)

I might have been mistaken for another person.

You probably mean "mistaken", not "misunderstood" (which would not be meaningful in this sentence).