One more point, (被)当成=1, sb is regarded as sth 2, someone assumed that...(by mistake)

Generally, 当=成为 while 成为 is more formal, if a woman just knowing she gets pregnant and says I am going to 成为 mother! This will be quite funny. But if this happens in a speech in public, "成为 a mother, for me, is quite meaningful"---this will be fairly good.

In this context( someone will play a role of mother--someone is pregnant), 当妈妈 is grammatical. But this can only be a phrase instead of sentence which will make sense. Hence, 我要 (wo yao, means I want or I will) 当妈妈了! is much better and can be understood. One thing quite noteworthy is 当 emphasize on the "role" or "position", eg: 我想当老师 (I want to be a teacher, 成 is completely inappropriate here) As for 成 , this focus more on 'become", "if you eat parrot even more in this way, you are likely to be a rabbit! 成 is proper here to replace "to be". I will not trust you unless I am a idiot. Here 成 is also proper. The above two examples, 当 are either not grammatical .

“当妈妈”是一个状态，比如“当妈妈真是一件不容易的事儿”="Being a mother ist a very difficult thing" 没有“成妈妈”这种说法，应该讲“成为妈妈”，强调动作或变化,=bekome。 但是很少见到带有“成为妈妈”的句子，即使是用在强调变化的地方，也会说：”我就要当妈妈啦“

I think if you include the question in sentense, it will be easy for others helping you.