The phrase "badge of infamy" is often used to describe something shameful or disgraceful. However, there are many synonyms that can also convey this meaning. Some examples include "stigma," "disgrace," "taint," "brand," "blemish," "mark of shame," and "infamous label." These words are commonly used to describe the negative consequences of bad behavior or a bad reputation, and can be used in a variety of contexts. Whether describing a criminal record, a public scandal, or a personal failure, these words all capture the essence of the original phrase and effectively convey a sense of shame or dishonor.