There isn't a lot of evidence either way for sense of Norman identity in Sicily. The best we can say really is that indications of Norman identity are conspicuous by their absence, and that the Mediterranean Normans adopted more local customs and practices than they brought with them from Normandy.

The earliest Italian Norman diploma (diplomata are official documents - charters, writs, etc) that I know of, issued in 1053 by Drogo (one of the first of the Hautevilles to migrate to Italy), opens in its second sentence with 'Ego Drogo ... dux et magister Italie comesque Normannorum totius Apulie adque Calabrie' (ed. Menager, Recueil des Actes des Ducs Normands d'Italie). This is Drogo describing himself as Norman count of Apulia and Calabria. No great surprise really, since Drogo was part of the first generation - those who actually lived in Normandy and then left to go south. What's more surprising is that even in the earliest of Robert Guiscard's charters in 1057 he makes no reference to being Norman, focusing instead on being duke of Apulia (Menager, Recueil). Like Drogo, Guiscard had lived in Normandy and so was actually a Norman, but based on the limited evidence available from his diplomata he didn't have a lot of interest in holding on to that origin.

Although Drogo and Guiscard are earlier than your question specified, I think it's worth making the point that these earliest Norman arrivals in Italy still didn't make much fuss of being Norman as far as we can tell.

Once you head into the 12th century the diplomata of Roger II and William I just don't mention the Norman connection at all. Where the diplomata of, say, William the Conqueror in Normandy describe him as dux Normannorum (duke of the Normans) the diplomata of Roger II and William I use terms such as rex Sicilie, ducatus Apulie and principatus Capue - king of Sicily, duke of Apulia and prince of Capua respectively (ed. Enzensberger, Guillelmi I Regis Diplomata). As an aside, it's worth noting how uncommon it is during this period for a European ruler to be described in their official documents as ruler of a territory rather than a people. 'King of the English', 'duke of the Normans' and so on are much more common. I attribute this to the diverse community of Sicily.

Of course, absence isn't strong evidence of anything but Dr Mark Hagger remarks that 'by the early years of the twelfth century, however, the first generation of Italo-Normans ... were referring to themselves as sons of Normans' (Hagger, 'Kinship and Identity in Eleventh-Century Normandy: the Case of Hugh de Grandmesnil, c. 1040-1098', Journal of Medieval History 32). There certainly seems to be something to it.

This is backed up by the culture of Sicily under the Hautevilles. There are reports of Roger II dressing in Islamic garb, perhaps partially because he spent most of his life and formative years in the strongly Arabic environs of Palermo. He was also educated as a child by a combination of his north Italian mother Adelaide and a Greek official named Christodoulos. His father died early on so it's reasonable to suspect that the Norman influence in Roger's upbringing was overshadowed by more Mediterranean ones. As count of Sicily, Roger recruited as his right hand a man named George of Antioch who might be North African or Byzantine in origin but certainly wasn't Norman. Again, no particular attachment to Norman officials or practices. Indeed, the mosaic of Roger II being crowned by Christ, still visible in the church La Martorana in Palermo, shows Roger clad in (outdated) Byzantine imperial garb. The mosaic was commissioned by George rather than Roger himself but I think it's fair to assume that George wouldn't have chosen this image if Roger was likely to disapprove. Roger seems to have been more interested in likening himself to eastern emperors than to anyone from his father's homeland.

There definitely seems to have been adoption of established non-Norman governmental practice in the region as well, rather than an import of such from Normandy. There are indications that Roger I (father of Roger II) adopted Byzantine tax practices that had been in effect in southern Italy since long before the Norman arrival, and the practice of recruiting secular notaries to administrative positions (rather than using clergy as in most of Europe) is definitely a Byzantine hangover. (The last couple of paragraphs are based mainly on: Houben, Roger II: a Ruler between East and West; Matthew, The Norman Kingdom of Sicily; Angold, Byzantium).

Perhaps most strikingly, when the Sicilian Normans did import practices from outside, the source wasn't Normandy or Norman England. Arguably the most prominent example is the diwan al-tahqiq - an Arabic-named office within Roger II's government which dealt with landholding and fief registry, and which Prof. Jeremy Johns argues at length was based on a similar office in contemporary Fatimid Egypt (Johns, Arabic Administration in Norman Sicily: the Royal Diwan). When Roger found himself in need of an administrative structure to use as a model for his own reforms, he turned not to Normandy or England but to Egypt.

There's a lot more that can be said about all of this, and I might come back later when I have more time, but hopefully that gives you something to begin addressing your questions.