User blog comment:Xilinoc/Ch. 576 - THE KILLERS HIGH 2/@comment-1338810-20140409140322/@comment-1338810-20140409220812

"A zanpakuto is one's unique self. It should be obvious why there can't be two people with the same zanpakuto, no matter what title they may be bearing."

There could be if one of the people was *dead* first. And who is to say that an inherited Minazuki would be exactly the same? There are after all multiple ways to write it.