"Be noised abroad" is a phrase used to describe something that has become widely known or talked about. There are several synonyms for this phrase, including "circulate," "spread," "propagate," "disseminate," and "publicize." Each of these words carries a slightly different connotation, but they all refer to the act of making information or news widely known.
For example, a new product launch might be "noised abroad" through a well-planned marketing campaign that "circulates" information through various channels such as social media, email, and advertising. Alternatively, a celebrity scandal might be "noised abroad" through gossip that "spreads" quickly through social networks and word of mouth. Whatever the context, these synonyms all describe the way in which information or news is communicated and shared widely with others.