1. Myth: Dragon appeared in Loguetown and Luffy was able to hear the dragon talking in the Apis Arc. The D must mean DRAGON.
Fact: The Warship Island Arc was not canon. Therefore everything in it (except for a few things like the Calm Belt information) was not written in the manga by Oda. This rumor was originally created by a popular anime blogger who took a wild guess after watching the arc. Due to the popularity of said blog, others also pondered on the idea (though some fans came to this meaning on their own accord). However, it has been proven Dragon has an important plot role.
2. Myth: It is the first letter of the civilization name.
Fact: We do not know what the D. means at the moment. This comes from the significant actions of the World Government to stop Clover saying the name.
3. Myth: It is not a D it is part of a smiley! Also, every D character that appeared in the series has smiled (even Portgas D. Rouge).
Fact: This one stems from the act of smiling upon death.
4. Myth: It is the name of the royal family of the lost civilization or a clan within it.
Fact: We do not know anything about their culture or if they even had a royal family.
5. Myth: D. means “Devil”.
Fact: This one is a nod to Devil Fruits. Rosinante did however state that those with the D. are God’s natural enemy, which is what a devil is conveyed as.
6. Myth: It means “Damashii”.
Fact: This one is linked to the talk of spirits and “will” throughout the series.
7. Myth: It is half a circle.
Fact: This one comes from “One Piece”, the speculation is that the D. is half a circle or pattern/symbol. In other words, acquiring Roger’s treasure will result in the symbol becoming “One Piece” again.
8. Myth: It means “Danger”. One of the Gorosei said so in Post-War Arc!
Fact: One of the elders really said that, but that’s due to the translation “D always means danger”, meaning that all of the people with D on their name were dangerous people.
9. Myth: It is given to those who can start a new era. Such as Roger starting a new age of pirates, and Blackbeards’s betrayal and Ace’s capture leading up to the Marineford War.
Fact: Portgas D. Rouge’s only (confirmed) significant act in life was giving birth to Ace.