Mercenary companies are usually little more than bands of low-level thugs. This one is a much more sophisticated organisation, with its own history, regulations and culture.
Surnames: The Chinese were among the very first cultures to adopt the use of hereditary surnames (around 2800 BC). But the custom didn't quite catch on in Europe - at least not until the Venetian aristocracy made it popular sometime between the 10th and 11th centuries AD. What culture made it popular in your setting and why?