The phrase "has a bad name" can be replaced with various synonyms depending on the context. For example, "has a poor reputation" can be used to describe a person or thing that is generally viewed negatively. "Is notorious" is another synonym that implies a well-known negative connotation. "Is maligned" can be used to describe something that is unfairly criticized or spoken ill of. "Is disreputable" is a slightly more formal synonym that implies a lack of respectability. Finally, "is stigmatized" is a powerful synonym that implies a negative label or mark that is difficult to overcome.