The sentence
I am not the person you think I am.
is most often used to mean "you have misunderstood my character", not "You have mistaken my identity." It is used when one person attributes to another characteristics that the second person thinks mistaken, as in:
Person A: You are much too kind to say such a thing.
Person B: I am not the person you think I am.
Often this is used in a gendered version, with "man" or "woman" used in place of "person".
When the intent is to indicate a confusin of identity, ther are many ways to express this, including several metioens inn teh comments to the question:
- That's not me, I'm Bob.
- [I think] you have the wrong address.
- I'm afraid you've got me mixed up with someone else
- There's no-one of that name here. You must have the wrong address
- I don't think I know you. I believe that you have he wrong person.
- Who are you looking for?
- I think you are mistaken.
along with many other possibilities.