We know that by the time Federick II ruled, the King spoke sicilian, but what about his grandfather, Roger II, for example?
The answer is immediately. The normans immediately sought to integrate themselves into the social, military, and political hierarchy in Sicily. I can't really add anything else without knowing what precisely you're referring to when you say "Distinct Identity," although you might be interested in this older answer of mine from awhile back which might offer some clarity on a few related themes.
On the topic of the social dynamics of the Normans "in the south," I wrote these past answers which might interest you: