I expressed my opinion on the comparatively simple case of the correct name of Tancredi Altavilla, but not all cases allow a simple answers. Let consider the case of another very famous king of Sicily and Emperor of Holy Roman Emperor: Federico , son of Costanza Altavilla (Aunt of Tancredi) and of Heinrich VI Hohenstaufen. He was born in Jesi (center of Italy on the adriatic coast) from a mother born in Italy (Sicily) in a family of normand origin and could speak fluently at least 6 languages: latin, sicilian (proto-italian language), german, arabic, greek, french, He was raised in Palermo (Sicily) till the age of 24, subsequently moving to Germany till the age of 32. Therefore Federico should be preferred as first name to Frederick (I re di Sicilia, II emperor of Holy Roman Empire ) while Hohenstaufen is correct as LNAB from his father's family name, transmitted to his successors. On history books he is also often referred as "di Svevia"( = of schwaben" as Hohenstaufens were Dukes of Schwabia). Federico was also re dei Romani,king of Jerusalem, king of Burgundy, etc.