"Not giving a damn" is a phrase that is commonly used to convey a lack of concern or interest in something. If you are looking for synonyms to use instead of this phrase, there are several options available. Some possible alternatives include "not caring," "not bothering," "not worrying," "not fussing," or "not paying attention." Other phrases that convey a similar sentiment include "blowing off," "shrugging off," "brushing aside," "ignoring," or "dismissing." These phrases can be used in a variety of contexts, from personal situations to professional settings, to indicate that you do not take something seriously or do not consider it important.