Short, Sweet, And Totally Rare, The Girls Name, Rim, Belongs At The Top Of Your List! Rim Has Roots In Swahili And Arabic And May Be A Short Form For Rima Or A Contraction Of Reem. Its Meaning, "white Antelope," Refers To A Beautiful Species Native To The Sahara Desert. Perhaps Your Darling Rim Will Form A Special Bond With Animals! Some Other Adorable Forms Include Rimah And Rimma.