Question

Since the rise of his designs, Frank Lloyd Wright _______ an icon of modern architecture.

Answer 1

Has become is your answer.

Answer 2

I'm not really sure what you need in this sentence. Is it a verb? Do you need to find the appropriate tense? If so, here is how I would do it:
Since the rise of his designs, Frank Lloyd Wright has been/has become an icon of modern architecture.
You should use the present perfect tense because this is an action that began in the past, but is still applicable in the present.