There might be multi-headed dragons. It's possible. But, in human form they would have only one head.
The extra heads wouldn't have their own personality. They would just be extensions of the dragon's body. It could talk through them, eat through them, use breath weapon and speak through them, but they wouldn't be independent personalities. They wouldn't argue with each other or debate about whether to eat someone or blast them with acid.
So, no: a multi-headed dragon wouldn't have multiple personalities in human form. Nor would they have three heads, as that would defeat the purpose of a human disguise.
edit - 1:52 PM, 4/27/2010 to include second question about multi-headed dragons.