Hello, I'd like to ask if both sentences sound correct? thanks.
1/ She wants to become a doctor.
2/ She wants to be a doctor.
Yup. They both sound just fine.
They both mean very much the same thing.
Possibly the first one stresses that her ambition is to go to medical school -- stressing the "becoming" part of the process. The second one indicates that she wants to live her whole life "being" one.
Yet there's not much difference in the end. Either one is fine.