There is no formal admission to become a Clansman of the Silver Clan. As Yashiro Isana said to Kuroh Yatogami, "There's no need for such ceremony for us to be friends."
In order to become a Clansman, the person only need to take the King's hand while he synced the person's bio-wave spectrum with the Silver Sanctum Spectrum, thus, granting the Clansman access of the Silver Aura.
Befitting the Clan's name, members possess a Silver Aura.
This aura allows the King immortality, inviolability, and the ability to manipulate gravity. The latter ability is presumably the only ability that Clansmen obtain, and gives them a sense of lightness. 
The White Rice Party Clansmen specialise greatly in agile, powerful movements to hit and evade their opponents, however their styles differ greatly. Kuroh is formally trained in kenpo, and his spatial hand works well as a longer-ranged attack. Meanwhile, Neko has had no formal training in combat, however her agile, flexible reflexes allow her to avoid many attacks and help in fighting one on one with someone, along with her illusions providing stellar defense. Shiro mainly utilises his umbrella in combat for defensive purposes.
The insignia of the White Rice Party is an emblem that was once a common symbol of royalty in Germany, specifically in the House of Habsburg. The Clan's version of it has "Weiß König der Silber" written, which vaguely translates to "White King of Silvers".
Kuroh established the Clan's name, at the request of Yashiro.