One either is or is not a dragon, and trying to "become" one is rather like trying to change sexes without the proper medical procedure. In short, people cannot "become" dragons.
However: This is not to say that dragons always know who they are! Very few are born with the knowledge of their inner draconity; most have to grow into it and discover it. Draconity is just as legitimate if discovered late in life. True draconity is not a "becoming," it is a "returning," and true dragons know the difference.
Ultimately, the question boils down to "How do I know if I'm a dragon?" (answered above). However, one can certainly join the dragon community whether they are a dragon or not (see next question). And many members of the dragon community "adopt a character" at the beginning of their stay -- but later grow to find that the "character" has adopted THEM.