One of the toughest parts of role-playing a non-human character is to give that PC a distinct cultural identity. We often play ever character of every race as if they were born and raised in the Human world. For many races this isn’t a big deal because their societies will parallel Humans’ in many ways. However, Drow are very different from Humans and this should be reflected in the way they are played.
Although your character is an individual and you have the freedom to play him as you see fit, it’s important to consider his upbringing and how that has shaped his personality and attitudes. He might have forsaken his heritage to become an adventurer, but if he was raised in Drow society there are a lot of little details that you should keep in mind when running him. Use these differences to make your Drow stand out from the Elves and Humans in the party.