Clench is a surname. Notable people with the surname include:
Andrew Clench (died 1692), English physician
Jim Clench (1949-2010), former member of the bands April Wine and Bachman–Turner Overdrive
John Clench (died 1607), English judge
Nora Clench (1867–1938), Canadian violinist
Ralfe Clench (c. 1762-1828), farmer, judge and political figure in Upper Canada
William J. Clench (1897-1984), American malacologist