How you pronounce the name depends a lot on where you come from and how you spell it.
Personally, in my family, we all say "Bee-yan-kee", but this reflects our Canadian English pronunciation.My father, who immigrated to Toronto from Italy when he was 20, says "Byahn-kee" as any native-speaker of Italian would.
While on a trip to Antigua, Guatemala, I ate at a restaurant called "Bianchi's".Everybody in town pronounced the name "Byahn-chee" reflecting the Spanish reading of "ch" as in English "chocolate".Argentinian friends of mine say either "Byahn-kee" or Byahn-chee".French friends usually pronounce our name "byawn-shee" again reflecting French reading of "ch" as in English "machine".
Some Bianchis get around this by changing the spelling of their name so that it can be pronounced more easily in their new country.In a Montreal phonebook, I found our name spelt "Bianki".I've also seen a Spanish version spelt "Bianqui".Both of these would reflect the original Italian pronunciation more faithfully.
In the end, unless you take the Italian pronunciation to be your yard stick, any pronunciation will do.After all, it's your name, isn't it?