the name of mine 还是the name of me

应该是the name of mine 和the name of the man's
这是名词的双重所有格的用法.
当名词前有冠词 ( a, an, the ),数词 ( one, two… ),指示代词 ( this, that, these, those ) 或不定代词 ( some, many, a few等)时,常用双重所有格来表示所属关系,即“of 短语 + 名词所有格/名词性的物主代词”.它具有强调和突出的作用.如 a friend of mine, two classmates of my brother’s, some books of hers, a few teachers of Li Ming’s, those notebooks of the students’.