Become is the most common compound verb in English, combining be with come. In fact, it's the most common 2 syllable verb. Its inflection follows come, i.e. it is an irregular lexical verb. It has the third person form "becomes", the -ing form "becoming"; and the irregular preterite "became", and an uninflected irregular past participle "become".
Become has obvious Germanic cognates, e.g. German bekommen; unfortunately in German it means "get" or "receive" and therefore is a false friend. For example, a German-speaking student may say #"I have become a letter" translating "Ich habe einen Brief bekommen", but meaning "I have received a letter."