Kinoe is the name that Tenzou was given by Danzou during the days when he was with ANBU Root. You could call it his first alias. Tenzou is considered his real name (the story of it all is told in some anime filler episode, but just roll with it.) Yamato is the alias he goes under when he enters Team Kakashi.
So his real name is Tenzou, but Yamato is the more common one used I don't really get it either.