Anyway, the "Green Lantern" name makes some sense once you know the whole backstory. From a marketing and branding perspective, however, there are tons of flaws. To wit...
* Who actually knows this backstory? Pretend Green Lantern existed in real life. One day, a green-suited superhero actually shows up and starts helping humanity. While there would no doubt be intense speculation about the nature of his hero's powers, the general public would know that this guy could a) fly, b) have green energy all around him and c) could use that green energy to create objects and whatnot. So, naturally, having "Green" in the name makes a lot of sense given the colour motif. The problem I see here is that the average person would have no idea where the "Lantern" part is coming from. Example:
Random person: Wow, thanks for rebuilding our dam and saving the town from flooding, mysterious superpowered stranger!
Green Lantern: Think nothing of it, just helping out those in need!
Person: Wow, whatever do we call you?
GL (with hands proudly on hips): The Green Lantern!
Person: ….uh, what?
GL: That's right, the Green Lantern! See, there's a little picture of a lantern here on my chest. I didn't draw the logo myself but still, it's pretty cool.
Person: Wait, what does a lantern have to do with anything? That ring you're wearing seems to be pretty clearly be your main deal, shouldn't we call you the Green Ring? Or Ringman, possibly?
GL: Nope, it's Green Lantern all the way.
Person: But that makes no…
GL: Look buddy, I fixed your damn dam, just go with me on this, okay?
I mean, it's possible that Hal Jordan/John Stewart/Guy Gardner/Kyle Rayner/any of the several earthlings who have held a GL ring at one time or another actually publicly explained the name and the whole power battery thing. Except…that makes no sense either, since why would you reveal your power source like that? Wouldn't your enemies then focus on finding this power battery and thus completely robbing you of your abilities?
Forget "the colour yellow" being a Green Lantern's weakness, which is stupid enough in itself --- the real weakness is that a Green Lantern is a completely mortal person who is totally reliant on the power battery in order to operate. Batman without his normal gear is only incrementally less dangerous. Iron Man without his armour isn't much of a threat, except at least there Tony Stark himself is still a technological genius who can whip some kind of makeshift device or weapon in a pinch. A Green Lantern without a working ring, however, is essentially useless. Why call attention to your biggest weakness in your very name?** Or, if the GLs just never explained their name, did the entire DC Universe collectively decide to just not ask about it since the Lanterns were being so cool about saving the world and whatnot?
* Who is supposed to be impressed by the name "Green Lantern"? It isn't intimidating, like Superman or the Hulk. It isn't descriptive, like Spider-Man or the Human Torch. As noted, it's a name that requires a lot of explanation, which immediately makes it a non-starter in terms of striking fear into the hearts of criminals. It doesn't even pass the bouncer nickname test. Say you're in charge of hiring a bouncer for your nightclub and you're told that your final two candidates have nicknames. One guy is known as 'the Punisher.' Yikes, that sounds like a guy who can take care of business, no question. The other guy is known as…you guessed it, 'Green Lantern.' What, does he shine a bright light into people's eyes to try and calm them down?
* If you're going to name yourself after your gear, why this piece of gear? As noted earlier by some random person, "Ringman" or "Green Ring" are more sensible names for a Green Lantern. Sure, you're again calling attention to the ring as the main source of your power, but in that case it's hard to avoid --- Green Lanterns in the comics are always pointing their rings at the bad guys to blast them with energy or what have you, though given the ring's wide scope, actually pointing your hand in the right direction seems redundant.
Naming yourself after your signature weapon is fine, in and of itself. "Green Arrow" is a perfectly decent name for an archery-centric superhero. "Doctor Octopus" has six mechanical arms, that checks out. Hell, I'd argue that Aquaman would be perceived as much less of a joke to the general public if his name was actually "Trident." But you're getting just a bit too obscure with "Green Lantern" especially when the actual lantern-shaped battery itself is rarely actually called a 'lantern.' I haven't read a ton of GL comics over the years but of the ones I have read, the power battery is just called….the power battery. Though it's a little abstract itself, I'd even consider that a better superhero name --- I'd be scared of a bouncer known as 'Power Battery,' wouldn't you?
If a new superhero called the Lightbulb or Captain Florescent was introduced today, we'd laugh it out of the building. Green Lantern is just as dumb a name, but it's been grandfathered in by 70 years of history. Green Ring forever, man.
** = This was going to be a footnote but it ran so long that I just stuck the whole thing at the bottom of the post as a dessert course, if you will. I've always been intrigued by the idea that comic book fans have a much wider knowledge of a character's powers than the characters themselves. How would you properly 'scout' a friend or foe in this world? Everyone would know that, say, Superman is hella-strong and can fly, but are lesser-known powers like the super-breath a known quantity? Like, you're a minor hero teamed up with Supes at some point and he just busts out a freezing-cold gust of wind to stop an oncoming tidal wave or something. You'd be like, "holy crap, where did THAT come from?" Fans can feel this way too, as I think everyone was pretty surprised during the old Christopher Reeve movies when Superman could suddenly a) erase Lois' memories with a kiss, b) throw a giant saran-wrap S from his chest emblem and c) somehow turn back time by flying around the earth so fast that it "reverses the rotation," which even in comic-book science is an affront to the physics.
Anyway, it would seem to aid a superhero if they didn't make all their powers so publicly known in order to give them an edge in battles. Green Lantern's odd name may actually help in this sense, provided that he never explains its origin. Interestingly, in modern comics, the hero with the best sense of keeping secrets about himself is Batman. I would presume that relatively few DC Universe characters actually know Batman doesn't have any powers, since he's so good about keeping up the mystique. One of my favourite character details of the old Grant Morrison Justice League comics was that the younger heroes (Green Lantern Kyle Rayner and the Wally West Flash) were kind of intimidated by Batman, despite his being their teammate and the fact that either of them could decimate Bruce in a second if it came right down to it. This is just more reason why Batman is the coolest.