There are several synonyms for the term 'having cover', each carrying their own distinct meaning and implication. Some common synonyms include concealing, shrouding, hiding, cloaking, masking, and screening. These words denote the act of keeping something obscured or hidden from view, providing a degree of protection or privacy. While they may be used interchangeably to some extent, each synonym reflects a slightly different nuance of the concept. For example, to conceal implies a deliberate effort to prevent something from being seen, while to shroud suggests a more mysterious or mystical quality. Ultimately, the choice of synonym will depend on the context and tone of the sentence or passage in which it is used.