ファミリーの名にかけて

Missing, extremely new, or very obvious to obtain.

Probably a reference to the 2010 Canadian documentary film of the same name. It explores the issues of honor killing (the act of killing a family member due to beliefs that such killing is necessary as retribution for the perceived dishonoring of one's family), particularly focusing on Aqsa Parvez. In Loothunt in Mazeville, after Trailblazers retrieve all the stolen goods, Aymille (the main NPC of the mission) expresses anger towards her father who had betrayed The Family and plans to capture him with her own hands. The chive could also just be that "In the Name of [insert name]" is a phrase commonly used as an action, declaration, or statement that is made on behalf of, for the sake of, or under the authority of someone.