This is point No. 1 in any debate about cloning. The process just copies a genome, and poses no worse a threat to the human sense of self than does any identical twin. From there things get complicated, though, and a new anthology of articles on the subject is meant to help navigate this weird, still-uncharted moral territory. The writers brood over the question of individuality and self in the aftermath of Dolly's birth in 1997. So far the debate relies on language borrowed from older arguments, like the ones over abortion or slavery.
Answers fall into categories.
Some writers can't get past the sickness of the idea of replicating a person. He will not be fully a surprise to the world. I've known Daniel Ellsberg for 25 years, and the new biography of the Pentagon Papers leaker is a hatchet job worthy of the White House Plumbers. If these walls could talk I made a joke about my transgendered co-worker's looks, and I'm afraid she overheard me.