No, not Keanu Reeves, just Reeve, which is one of those rare names that sounds appealing, and you have to say it out loud. It is a Middle English occupational name meaning "bailiff." Not the worst I've heard, and better yet, there's no rule that says you need to go around telling everyone what your baby's name means. And if you do, no one's going to say, "Oh, how horrible." There is actually a rich medieval history (including one of the stories in The Canterbury Tales) with a long list of duties a reeve held, and it was in fact a high position. I believe in part they later became sheriffs.
An alternate spelling is Reave, and there are dozens of namesakes with Reeve or Reeves as a surname. Two familiar namesakes other than Keanu Reeves are Reeve Lindbergh and Christopher Reeves (but don't let the associations deter you, it's just one distant recollection). Reeve is very similar to the French word for "dream." It is also similar to other popular names like Reid/Reed, Rhys, and Reese/Reece.
Not on the top 1000, and I don't believe it ever has been. In 2010 there were just 21 baby boys named Reeve, 18 named Reeves, and none spelled with an a (Reave, Reaves). In 2011 there were 12 Reeves and 33 named Reeve.