Solution 1:

Syntactically, "what" is a direct object. To realize this, replace "what" with "many things', for example.

"She has been called many things".

"Many things" is also a direct object.

Some people might consider that "what" or "many things" in the sentences above are not direct objects but "predicative" constructions, especially if they consider that the verb "call ..." by itself doesn't provide enough meaning to the sentence (i.e., it is working as a "linking" or "copulative" verb).

But I don't think that is the case.

Semantically, "what" is an interrogative pronoun.

BTW, "what" is not a relative pronoun (or relativizer) in that sentence.

In order to be a relative pronoun, it should have been linking an inner sentence with the main sentence, in a "relative capacity".

For example, in the sentence:

She was called what I suspected she would.

"what" is a relative pronoun.