First of all: There is nothing wrong with choosing your own name. There are many examples where this worked very well, look at our very own Phil Morse.
However I think choosing a DJ name is important early on, as you want to start promoting yourself as soon as you hit the street and many people will remember you from your early days.
Of course this can also be something of a let down if you change genres completely etc.
As in my case, I was an Industrial DJ for like 10 years and my DJ name well known in that scene, after I came back from my break, while I still listen to Industrial sometimes, my focus shifted largely. So I had to chose a new DJ name and hence I became “Terry 42”. It worked out pretty well for me and if I know my history there are several successful DJs that did the same.
So bottomline is: I think you should chose early on, but if you decide to make a huge bend in style or sound, do not be afraid to change your name.