I believe the “D” in names stands for Destiny. If you look closely, every person with the “D” in their name has a significant destiny, a strong backstory, or an important role in the world. Many of them are powerful figures who have had a major impact during their lifetime. What’s interesting is that most of the people with the initial “D” also seem to oppose the World Government in some way. They either resist its rules or have a strong, free will, remaining uninfluenced by it.
The Five Elders seem particularly bothered by the people of “D” because many of them end up being their enemies or challenging their authority. During Episode 1071, when Luffy awakens Gear 5, the Five Elders discuss how the Gomu Gomu no Mi (Human-Human Fruit) always slipped through the World Government’s grasp. They even mention how the fruit seemed to evade capture, which reminded me of how Shanks (who I suspect also has a “D” in his full name) stole the fruit from the World Government and brought it to Luffy’s hometown. Shanks, of course, was once a disciple of Gol D. Roger.
My theory is that people with the “D” have been unknowingly acting as guardians of the Gomu Gomu no Mi for centuries. Their ultimate mission seems to be helping the fruit find its way to Joyboy’s reincarnation—Luffy. That’s why I think “D” represents destiny. These people are destined to answer the fruit’s call, ensuring it never falls into the hands of the World Government. They also help the fruit reach its true purpose in reviving Joyboy. To do this, those with “D” must be strong warriors, nonconformists, and people with great willpower, like Blackbeard, Rocks, Roger, Dragon, Law, or Saul.