The X-Men are a great example here, since they have fewer reboots and retcons than the general comics population.
The '60s team (Cyclops, Marvel Girl, Iceman etc.) had secret identities, with the old boring plot lines about whether people would find out about their normal boring lives.
The '70s and '80s team (Storm, Wolverine, Rogue, etc.) are like rappers: they have code names for public appearances, but their real names are public knowledge. Most of their friends are also Marvel characters or halfway across the world, so they don't need to worry about putting people in danger. Jean Grey's roommate is dating Iron Fist, Nightcrawler's girlfriend is a witch who helps the X-Men just as often as she gets kidnapped, etc. Note the switch from "Marvel Girl" to "Jean Grey" to "Phoenix".
The '90s and '00s teams basically treat a superhero name as a rite of passage, like a fraternity nickname. With more of a focus on the school, you get the impression that the name you pick at age 14 to make your dumb power sound awesome is the name you'll be stuck with for the rest of your life. The people with dumb super hero names use their real names. As Wolverine becomes less ferocious and more responsible, people start calling him "Logan", while as Kitty Pryde grows up and becomes cooler, people start calling her "Shadowcat". (No one, not even in the comics, could ever call her "Ariel" with a straight face.)