There are different ways of saying that someone has become famous.
We can use “by”, “for”, “because” and “when”.

• “By” and “for” express the reason of becoming famous.

To use “by” and “for”, the verb must be in the past continuous :
eg. I became famous by singing. I became famous for singing.

• “Because” also expresses the reason of becoming famous.

To use “because” the verb must be in the past simple :
eg. I because famous because I sang.
or you can use “because of” with the past continuous :
eg. I became famous because of singing.

• “When” expresses the moment/the place of becoming famous.
eg. I became famous when I sang. (past simple)
or I became famous when singing in Manchester. I became famous when singing in December.(past continuous)