At the same time, your name is associated with the identity you've built up and hyphenation allows you to respect that while also respecting tradition and your husband's family's identity.
与此同时,你的名字与你建立起来的身份相关联,而连字符的使用让你在尊重这一点的同时,也尊重传统和你丈夫家族的身份。
省略形式的对比状语从句,完整形式应为 "while you are also respecting tradition and your husband's family's identity",主语 you 和系动词 are 被省略,保留现在分词 respecting。while 在此表示 "同时" 的对比/让步意味,强调在尊重个人身份的同时也尊重传统。