We all like to make our "Nice house, nobody home" and head injury jokes about Wonder Woman's boyfriend, but the truth of the matter is that he's not meant to be an especially stupid person. He can be a bit slow sometimes, and he's certainly mockable for it, but he's not actually unreasonably stupid about the secret identity. Yes, this man is completely in love with Wonder Woman but does not recognize Diana Prince. There's an interesting metatextual aspect to this, but Marston was a very smart man who actually included an in-story reason for Diana's secret identity being secure.
See, the thing everyone conveniently forgets is that there actually was a Diana Prince in the Golden Age. She's the Pauper in our Diana's Princess and the Pauper style origin story. Diana Prince has a job at the hospital and a man who's going to move to South America, but she doesn't have the money to join him. Princess Diana has the money, but she's really got no home, no job, and no way to keep an eye on her danger-prone love interest while he's in the hospital. So one Diana helps the other out, and manages to get a quiet place from which to observe Man's World.
A lot of people hate the secret identity, I know those are the stories where Diana looks the worst in the Silver Age (but they are also the sort of stories where CLARK looks the worst in the Silver Age), and I actually do like emphasizing Truth and Honor as what Diana represents among superheroes. But if we have to have one (and for some reason they seem insistent upon it), I prefer the story where she comes up with it herself while helping another woman out. It's certainly better than "Batman set it up for her."
"But RAAAAGNELL! It's too implausible that she'd find an EXACT lookalike."
The gods have taken an active role in Diana's life. This isn't "Magneto's magnetic powers are allowing him to control stuff that can't be magnetized" implausibility, this is "What the fuck? A Steve Trevor from an Alternate Universe breached the wall between realities at the EXACT SPOT his recently deceased counterpart landed years ago, the DAY after Diana's memory of this universe's Steve has been erased" implausibility. This is a "part of the plot, and showing the mysterious works of Fate" coincidence, the sort of coincidence that is perfectly in keeping with her fairy tale/fantasy setup, having Hermes the god of chance meetings as a patron, and knowing that the Fates have woven this meeting into Diana's life.
But how does this make Steve less dense? Well, Nurse Prince worked at Walter Reed. Steve Trevor is based in Washington and has probably been in and out of that hospital a few dozen times for physicals, checkups, and minor injuries. He may not have ever talked to Diana Prince, but he's probably seen her around. And this is an established woman with a paper trail, a birth certificate, a diploma from a nursing school and (by Kanigher's retelling) a picture of herself standing next to Wonder Woman.
Along with not realizing there was once another Diana Prince peopel also tend to forget that Wonder Woman's real name isn't Diana Prince. (At least, they do when tagging on Tumblr.) It wasn't pre-Crisis, and it's not now. She is simply not that person. She has an origin that involves being raised on Paradise Island at the same time that Diana Prince was growing up in the US. While Diana Prince was establishing her paper trail, being photographed, meeting people that a private investigator can track down and talk to, Princess Diana was on Paradise Island. And while some people may doubt that the Amazons exist and their princess never set foot on US soil until the day she dropped of Steve, there's one person who has seen and spoken to them and knows that girl never saw a man before he showed up.
Steve Trevor is the only man on the planet who can be absolutely certain of where Wonder Woman came from, and he knows it's not the hospital on Diana Prince's certificate.
But why does he insist one is more attractive than the other? Well, he's pretty dazzled by Wonder Woman and it goes much deeper than her having a pretty face. He's wowed by her strength, capability and energy, traits that are hidden when she shows up as Diana Prince.