While we're on the subject of Noble Families, what is the story with Byakuya giving Renji this?

I thought the Ginpakukaza Haru No Usugime was an heirloom that was passed down to the successors of the Kuchki family name????? Did he just adopt him too and declare Renji to be his Heir? Boy if his family had problems with him adopting Rukya, they must love this action!