For the sake of plot, I am sure there is more than one operative in the employ of the Alliance. Heck, The Operative could have been a genetically engineered passel of clones if'n they wanted to use the same actor and a "Didn't I kill you already?" reaction from Mal.
That makes a lot of sense, actually. Why try to hide or change or erase a man's identity, when you can just grow him in a lab, and never give him a Birth Certificate? And no one will ever recognize him from high school.
I was also annoyed that Mal didn't finish the job, before he climbed out to that generator/computer platform thing. But the failure to kill him at the training house was understandable. He had just been thrashed, his eyes and ears must have been ringing from the explosion, Alliance goons were about to come down on him, and his last attempt to kill the Operative had been futile. It was time to clear out without further ado.
I was just delighted to see Mal shoot him as swiftly as he did, that first time. Most movies would have had the Op draw his hidden gun, and then the two would have spoken at some length, as if an aimed gun is just an idle threat, rather than a clear and present danger to be eliminated toot sweet.