You must be wondering who I am.
I think "who" in the object and therefore it should be "whom"? But for some reason, "who" sounds more natural to me.
What's the correct option? And why?
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"To be" doesn't take an object. If you say "I am a fish", the noun phrase "a fish" is the complement of the verb "am", not its object.
Traditionally, the complement of "to be" is in the subject case: "It is I". Colloquially, the object case is much more common and completely acceptable: "It's me".
In the case of "Who is it?" or "Who am I?" or "You must be wondering who I am", traditional prescriptive grammar and colloquial usage are in agreement (since "whom" is very rarely used in informal English at all).
So, whereas with "It is I"/"it's me" there is a conflict between old-fashioned prescriptive grammar and common usage, here "who" is unambiguously both correct and idiomatic, and "You must be wondering who I am" is the only option.
"Whom" here would be a hypercorrection typical of someone is trying to sound pompous but who doesn't know the correct grammatical rules.