Coming from an Anglo (I'm American) culture, when I study the history of England, it isn't until the Norman invasion that names I really recognize (Henry, William, Robert, Richard and so forth) start popping up. That being said, I didn't notice the name "Drogo" much at all if any during the conquest, although it seemed to be pretty popular among the Normans on the continent just prior. Was it just that there weren't many "great" Drogo's afterward so the name, although in use, had a steady fade into obscurity? If so, how long was it in circulation? Same goes for Tancred and to some degree Bohemond. These are pretty awesome names and I'm looking for why they faded out and if there is a notable end to their usage in England and England's territories.
You're absolutely right that names like Henry, William, Robert, and Richard only show up after the Norman Invasion simply because they're French names. More specifically, they're Christian French names. Until the 11th century a lot of the Norman families, including the Dukes of Normandy had Norse names like Rollo and Vilhjálmr, meaning 'Robert' and 'William' respectively.
But the greatest reason why the line of William the Conqueror never used names like Drogo or Tancred is that they came from a different family. Drogo and Tancred were of House Hauteville, a Barony of Normandy, while William the Conqueror was of House Normandy.
The Norman Conquest of England was led by the Dukes of Normandy, the Norman Conquest of Italy was lead by various nobles of Normandy, but chiefly house Hauteville.
TL;DR Names like Richard, William and Henry persisted in post-Norman Invasion England because those were the names of the conquerors. Names like Tancred, Drogo, and Bohemond briefly persisted in the Italian kingdoms following the Norman Conquest of Italy because they were the names of those conquerors.
While I cannot say much for the English usage of these names, you can find all three names used commonly in the other great Norman kingdom of the Middle Ages: the Kingdom of Sicily, and it's rulers the de Hautvilles! The sons of Tancred de Hautville would lay down the foundations for the Norman Kingdom of Sicily first as dukes and counts (including his son Drogo), and Robert Guiscard, eldest son of Tancred's second wife, would have a son who would later become Bohemund I, king of Antioch.
I would highly recommend John Julius Norwich's two-volume work, "The Normans in Sicily," as it's a great primer work on the topic, and it seems like it's too often that the Norman Kingdom of Sicily is overlooked so often when some of them would become the greatest adventurers of their time.