The phrase "don't give a damn" is a common expression used to convey a sense of indifference or lack of interest. However, there are many synonyms that can be used in its place. Some of these include "don't care," "not bothered," "unconcerned," "uninterested," "apathetic," "detached," and "nonchalant." Each of these words adds a slightly different shade of meaning to the phrase, but all convey a similar idea of a lack of emotional investment or concern. Whether used in casual conversation or in more formal writing, these synonyms can help to convey a speaker's attitude or mood.