"Under the name of" is a common phrase used to indicate the identity or ownership of something. However, there are several synonyms that can be used in place of this phrase. For instance, "known as," "called," "labeled," "termed," and "referred to as" are some alternatives. For example, "The book was published under the name of John Smith" can be rephrased, "The book was published as John Smith," "The book was called John Smith," or "The book was labeled John Smith." Using synonyms is a good way of avoiding repetition and making a text more interesting to read.