Disclaimer: I do not own Stargate.
He was called many things by many different people.
Dr. Jackson. He wanted to be called this for so long. All of those years of school so that strangers and colleagues alike would know that he was smart enough, that he could be taken seriously. He doesn't introduce himself this way off-world, though. Not many societies know what it stands for, how much it means to him.
Dan'yel. Sha're called him this. All of the people of Abydos called him this, but whenever he remembers it is always Sha're speaking. My Dan'yel. He thought about teaching the others how to say it properly while he taught them English. They pronounced it like it was Abydonian. They made him Abydonian. He was accepted whole heartedly into their society and could not bear to lose this one tangible piece of proof that he belonged.
Danny. His parents always called him this. After they died, he wouldn't let anyone else call him this. Being called Danny made him feel like a child. It reminded him that he was younger and smaller than everyone else. Except, Jack calls him Danny sometimes. It bothered him at first, but the other man doesn't care. Jack still calls him Danny and he finds that he doesn't really mind it all that much. When Jack calls him Danny-boy on the other hand…
Son. His parents were the first to call him such and for a long time, they were the last. Kasuf called him the Abydonian version, and he is also dead. He remembers the first time General Hammond called him son. It shocked him until he realized that was Hammond's way of saying he was fond of him. They still speak sometimes, though most of the time they write each other letters to catch up. The word son is in every letter.
Spacemonkey. Just what Jack was thinking when he stuck this name to him, know one really knows. Except maybe Jack, though that is still not a given. All Daniel can imagine is that he was just so happy that 'Spacemonkey' had escaped the explosions. At the time, Daniel was just as excited to see them too that he ignored the nickname. Hindsight is 20/20.
Karlin. He doesn't like to remember this name. It was given to him after his own name was taken from him. He was honored to work to help his people. He knew Jonah, Thera, and Tor, but did not know them. Later, he remembered how even though he didn't really know them, he couldn't help but be drawn to them anyway. They were his team after all.
Arrom. Another name he doesn't like to remember. Another time when his name and memories were taken from him. Except this time, he was being punished. This time, it was because he was a good person. Someone who couldn't stand idle while others suffered. Except he didn't know that. He only had the vague sense of somehow deserving this. He told Sam, as Arrom, that he wasn't sure if he would like the person he was. She told him he was wrong and now he knows that.
Tau'ri. He was only called this by Gould after being captured. They always spat it out with such malice, but he has never thought of the term as a bad thing. All of the Gould he really needed worry about knew him by name.
Sunshine. He was going to strangle Cameron Mitchell. Or maybe shoot him. That would be much easier, but not nearly as satisfying as wrapping his hands around the other man's neck. But in the end, he settles for a severe glare with just enough of a threat behind it that Mitchell only uses the name once in a blue moon. That doesn't stop Daniel from making sarcastic comments when, once again, the younger man is found captured without pants.
Darling. It was ironic. He had always hated it when Vala called him that. He tried to stop her, but it would only encourage her to use it further. He ended up just ignoring it and rolling his eyes. But, it grew on him, like she did. Now, he waits for it. Listens to hear it roll off her tongue. Knows that it is only for him. Now he loves it, just as he loves her.
Daniel. His name is Daniel. He has been called many things by many different people, but he is always Daniel. This is what he tells people to call him. It is his name after all and he likes it.