Greta wants to become a teacher. If someone or something becomes a certain way, they start to have that quality. When did you first become interested in politics? The past tense of 'become' is became. We became good friends at once. The smell became stronger and stronger.
to come, change, or grow to be (as specified): He became tired. to come into being. look well on: That gown becomes you. to be suitable or necessary to the dignity, situation, or responsibility of: conduct that becomes an officer. be the fate of: What will become of him?
Also in Early Modern English, become (and certain other intransitive verbs, such as come and go) used the auxiliary be rather than have for perfect aspect constructions.