one kanji from a nobleperson's name
Historical term referring to a single kanji taken from the name of a nobleperson (often a shogun or daimyo) and granted to a vassal as an honor. The recipient would incorporate this kanji into their own name. Cross-referenced with 偏諱を賜う means 'to grant a kanji from one's name'.
See also: 偏諱を賜う
The shogun granted a kanji from his name to his vassal.
The kanji '家' in his name is a granted character from his lord.