I was thinking about that when I was setting the very first demo but I decided to keep to a set name because Luke isn't a blank slate character. He has a past and personality. He knows a lot more than the player and he shares that over time, at his own pace. The player only helps him make decisions in the frames of how he's pre-established.
But I saw a few people saying that they hoped to name Luke so someday I may make a poll about that and possibly add that option to be unlocked very early in the game, depending on the results...