Uncanny Antman said:
I dunno...I kind of figured that it was symbolic of where he is in life now. His acceptance of the name Henry would come from bonding with his father years earlier, and I can imagine it healing the old wounds that led to him adopting "Indy" in the first place*.

Characters can grow and change, even if fans often don't want them to. :)

*Though I haven't seen a lot of the Young Indy Chronicles, so I have no idea when the name was introduced in those stories.

From what I recall, he adopted the name before he had a falling out with his Dad. But in any case, I think it's one thing to have a character change over time, it's another thing for a titular character to no longer use his name. Why not call the movie, "Henry Jones, Jr. and the Kingdom of the Crystal Skull"?