Origins
Multiple Proposed Origins for the sì Branch
For the sì branch, three origins are proposed: it may descend from the Warring States-era author 俟子, may derive from the Mi surname, or may come from the ancient Xianbei; the page explicitly preserves the uncertainty with “its origin is not uniform” and the cited formulations.
Reference: 俟姓_俟姓的来源和历史_百家姓
Historical Records
Documentary and Name-Change Records
The page says that the Zheng Tongzhi, “Clan Treatise,” records the 俟 surname, and relays accounts that the Northern Wei emperor Xian’s younger brother’s 力俟亥氏 later became 俟, while 俟奴氏, 俟畿, 俟伏斤, and 俟力代 also became 俟; these are retellings on the page, and the original sources were not verified in the supplied material.
Reference: 俟姓_俟姓的来源和历史_百家姓