Barry: Call me Barry or Flash, Bart. "Grandpa" makes me feel old.
And sure enough, not three sentences later do we see that he's dropped it. Considering that Geoff Johns is also writing the new Flash ongoing, it'll likely continue there.
Superman rarely refers to his archnemesis as anything but Luthor. This is also true for everybody who thinks he's a bad guy. Mercy, who loves him, but is employed by him calls him Mr. Luthor.
Post-Crisis Luthor always insisted his lackeys and conquests and pawns—and Lois—call him Lex, which just made him that much creepier.
In ClanDestine, almost all of the Destines address and refer to their father by his first name. The exact reasons are never spelled out, but given that he only seems to have raised few of his children, looks younger than most of them, and that some of them have quarreled with him, it's not that surprising. Not to mention that most of them have established false identities complete with histories that include fictional parents, and might not want to break their cover by calling Adam their dad when someone might hear... The only exceptions are Albert and the twelve-year-old twins.
Almost everybody refers to Dr. Charles Xavier as "Dr. Xavier" or "Professor." Notable exceptions are his love interests and Magneto.note But I repeat myself. Similarly, the Professor is one of the only ones who may refer to Magneto as "Magnus" (or "Erik" in the films).
The other notable exception is Wolverine, who refers to him as "Charley" until the Professor finally begs him to call him, "Professor, Professor X, Xavier, or even Charles, if you must." Wolverine replies, "Sure, Chuck."
The list of people on a first-name basis with Wolverine ("James") starts with Squirrel Girl, and ends very shortly thereafter. Even his wives tend to call him "Logan".
Superman and Batman will commonly refer to one another as "Clark" and "Bruce" while out of public earshot. Their use of one another's given names depends heavily on the story: In Batman: The Dark Knight Returns, Superman's use reads as a seemingly genuine appeal to reason, while Batman seemingly doesn't want to pay Superman the compliment his title entails. In Kingdom Come, Superman asks his allies to refer to him as "Kal", due to his increasing distance from his human nature. Bruce continues to call him Clark nontheless, both for snark and to remind him who he's meant to be.
Batman villain Tommy Elliot, AKA Hush, being Bruce's best friend from childhood, usually refers to him by his first name when the two face off. Batman commonly does likewise.
Dr. Light and Dr. Wily in Mega Man call each other by their first name even after Wily goes down the path of evil. This is mostly due to the long-standing friendship they had before their falling out.
A somewhat common trope in superhero comics as a tool to show intimacy between characters. This is less about being permitted to use someone's real name as knowing what it is to begin with.
If Reed Richards and Doctor Doom ever call one another by their first names (and they do, very rarely), something is very wrong. Recent years, though, have Reed bucking the trend and tending to call him "Victor" more these days, while Doom only calls him "Reed" when he's truly up the creek and needs an out.
Similarly, Doom in all his old world regality will only call the other three by their full first names. And if someone calls him "Victor," they either knew him in the old days or do it to get under his skin.
In fact, it was a long-running subplot in Young Justice that Robin couldn't give his real name to his friends, because knowing who Robin is might lead to finding out who Batman is.
When Tim Drake, the third Robin, first started dating Stephanie Brown (AKA Spoiler), he wouldn't give her his real name for the same reasons. When she complained about having to use a codename for her boyfriend, Tim noted that at least Robin was an actual name, instead of something like Green Arrow or Superboy.
One of Nightwing's civilian girlfriends presented a semi-aversion, which was mildly off-putting for some readers. She insisted on referring to him as "Richard," when he had spent his entire life (that's more or less constant monthly publishing since 1940) going by "Dick." To no one's surprise, she didn't last long.
Actually impossible for Apollo and Midnighter from The Authority, because they don't have real names - we see their identities being erased during a Flash Back in their first appearance.
Amongotherreasons, Damian Wayne was disliked at first is because he refers to beloved family butler Alfred as "Pennyworth." Even after becoming more liked, this isn't entirely dropped.