Gorenshi refers to brothers of prestigious families such as the Imperial Family and families of kuge (court nobles) and seii taishogun (literally, "great general who subdues the barbarians"), and so on.
Especially in the Edo period, it referred to daimyo (a feudal lord) who moved out from the Tokugawa gosanke (three privileged branch families of Tokugawa) and founded its own domain. Families of gorenshi used the surname of Matsudaira. When gosanke did not have an heir, a new lord of the gosanke was sometimes selected from this gorenshi.
Renshi (or gorenshi) of each family
Renshi of the Owari Tokugawa family
The Matsudaira (Owari) family of the Takasu Domain: Mitsutomo TOKUGAWA gave a part of their fief to his second son, Yoshiyuki MATSUDAIRA. The Matsudaira (Owari) family of the Yanagawa Domain: Mitsutomo OWARI (or Mitsutomo TOKUGAWA) gave bunpo to his third son, Yoshimasa MATSUDAIRA. The Kawatakubo Matsudaira family: Mitsutomo OWARI gave bunpo to his 11th son, Tomoaki MATSUDAIRA..
Renshi of the Kishu Tokugawa family
The Matsudaira (Kishu) family of the Saijo Domain: Yorinobu TOKUGAWA gave bunpo to his second son, Yorizumi MATSUDAIRA. The Echizen Nibu Matsudaira family: Mitsusada TOKUGAWA gave bunpo to his third son, Yorimoto MATSUDAIRA. The Kazurano Domain: Mitsusada KII (or Mitsusada TOKUGAWA) gave bunpo to his forth son, Yorikata MATSUDAIRA (later Yoshimune TOKUGAWA, the eighth seii taishogun). The Takatsukasa Matsudaira family of the Yoshii Domain: Nobuhira TAKATSUKASA, a younger brother of Takako TAKATSUKASA, a lawful wife of Iemitsu TOKUGAWA (the third shogun), took Matsuhime (Princess Matsu), the second daughter of Yorinobu TOKUGAWA, as his lawful wife, and was given the surname of Matsudaira as renshi of the Kii family. The family had their shikoseki (anteroom seats for feudal lords and direct retainers of the shogun at the Edo-jo Castle) in the Upper Room of the Great Corridor, which was allowed only to the families with the highest status in the renshi.
Renshi of the Mito Tokugawa family
The Matsudaira (Mito) family of the Takamatsu Domain: Yorifusa TOKUGAWA gave bunpo to his oldest son, Yorishige MATSUDAIRA (an older brother of Mitsukuni TOKUGAWA). The Moriyama Domain: Yorifusa MITO (or Yorifusa TOKUGAWA) gave bunpo to his forth son, Yorimoto MATSUDAIRA. The Matsudaira (Mito) family of the Hitachi-fuchu Domain: Yorifusa MITO gave bunpo to his fifth son, Yoritaka MATSUDAIRA. The Matsudaira (Mito) family of the Hitachi-shishido Domain: Yorifusa MITO gave bunpo to his seventh son, Yorikatsu MATSUDAIRA.