Rui is a Portuguese first name, also spelled Ruy. It has the same origin as Roderick and Rodrick. People with the given name Rui include:
Rui Almeida Monteiro (born 1977), Dutch footballerRui Barbosa (1849–1923), Brazilian diplomat, writer, jurist, and politicianRui Campos (1922–2002), Brazilian footballerRui Correia (born 1967), Portuguese football goalkeeperRui Costa (born 1972), Portuguese football midfielderRui de Figueiredo (1929–2013), professor, engineer and mathematicianRui de Pina (1440–1521), Portuguese chroniclerRui Falcão, Brazilian politicianRui Faria (born 1979), Portuguese football coachRui Jorge Faria Azevedo (born 1980), Portuguese football goalkeeperRui Alberto Faria da Costa (born 1986), Portuguese cyclistRui Jordão (born 1952), Portuguese football strikerRui Jorge (born 1973), Portuguese football backRui Machado (born 1984), Portuguese tennis playerRui Nereu (born 1986), Portuguese football goalkeeperRui Patrício (born 1988), Portuguese football goalkeeperRui Rio (born 1957), Portuguese politician and Mayor of Porto (Presidente da Câmara Municipal)