If I remember correctly, an important plot device in the He-Man animated series was that no one knew He-Man and Prince Adam were the same person (except for Man-At-Arms, Sorceress, Orko and Cringer).
Is there any explanation for why He-Man’s identity is a secret?
More importantly, is there any explanation for how He Man's identity is a secret? Adam and He-Man look practically same, except may be He-Man has less clothes.
No explanation is ever given in canon.
One popular explanation, however, relies on the act that the hero (He-Man, in this case) puts up as the civilian (Prince Adam). In the minds of those around him, He-Man is defined by strength, both in the literal sense and in the sense of his character. He's reliable, he plans carefully (and knows when he needs to consult better minds than his), he's brave, he's strong and fit, and so on.
Prince Adam isn't evil, but in the minds of those around him, he is defined by weakness. He's irresponsible and careless. Cringer helps the act along, by playing at weakness in areas that Adam cannot: he's notoriously cowardly and lazy, and because he is Adam's constant companion, Adam becomes associated with those weaknesses even though he doesn't necessarily have them himself.
In the face of such contrast, it becomes hard to believe that these people are one and the same. Of course they look similar, but come on; He-Man is strong. Prince Adam is weak. Everyone knows you shouldn't judge a book by its cover, and you only have to look a couple of pages in to see how different they are, so why bother finishing Adam's book? It's not very likeable anyway.
And that's exactly what the act is designed to make people think. In some ways, you could argue that this subverts some of the lessons that the story aims to teach, because if people tried to judge them by looking, it would be clear that they were the same person. Or you could argue that this illustrates the need to look deeper: sure, people could stumble across the truth just by looking, but that's only a coincidence. People don't figure out that Adam is He-Man because they don't like Adam, and so even if they look past the surface, they stop looking before getting very far past it. And that's why they wind up not seeing the truth.
It is true that in the original show, Prince Adam looks almost identical to He-Man, save for the costume change that happens during his hero-transition. Similar to how in the old Super-Man show, Clark Kent looks almost identical to Super-Man, leading one to think that people in the 80's must have been very easy to fool.
This is mostly due to a low-budget production, and the assumption that kids won't get things that arent' spelled out for them - the characters are clearly supposed to not be able to recognize the two are the same, but no attention is ever drawn to how alike they look.
In the 2002 TV series, the artists make more of an attempt to distinguish Prince Adam from He-Man. Their body size for one is drastically different, and despite both having short blonde hair, it's in a different style depending on which persona they're taking on at the time.
And before you ask, He-Man essentially looks the same as he did in the original run.
Nobody could mistake the scrawny kid with slightly messy blonde hair for the buff adonis with wavey blonde hair below.
As for WHY Adam poses as He-Man...
I don't know the original series well enough to say, but I'd hazard his reason for keeping it secret is the same both in the original and in the 2002 remake.
TLDR
The fact that there's no visual difference between He-Man and Prince Adam in the original series is a product of the time, and was differently portrayed in later versions of the character, but the reasons for the secret remains the same.
I don't think it is ever properly explained as to why his secret identity is kept a secret. In most cases, a superhero keeps their identity a secret in order to protect their loved ones, it's probably the same here.
If Skeletor and the lads knew who he really was, no doubt they would go after his friends and family.
As Adam, He-Man lacks the power and freedom from his royal responsibilities to effectively serve as Eternia's champion, and he is forbidden to transform when it might expose his secret. Thus, He-Man's greatest liability is the possibility that he will be trapped as Prince Adam during a crisis. Additionally, Adam must act irresponsible and careless to dissuade anyone from suspecting his dual identity, causing his friends and family to express disappointment in him. source
UPDATE
There is an interesting trope called Clark Kenting which covers this exact issue. He-Man is directly referenced under the Western Animation section.
He-Man looked exactly like Adam with less clothes and a tan.
This could be a possible reason.
There are many times where one of Skeletor's minions, especially triclops' machines, infiltrates the castle for espionage purposes. If Skeletor and his minions knew Adam was He-Man, he would never be able to leave the castle without them knowing, going to castle grey skull wouldn't an option, basically their goal would to always single him out trying to catch him off guard before he could turn to He-Man and never letting him leave. When Adam leaves the castle no one cares, but if they knew He-Man was leaving the castle they could always follow him to figure out what he might be doing.
Queen Marlena knew. She tells Adam that a mother always knows his son, and she untied Adam in "Rainbow Warrior".
Princess Janice from 'A trip to Morainia' saw him transform into He-man to defeat the spider, and later tells Adam what a great thing he did. Luckily no one listens to their sister, which was a theme for the episode, so Prince Adam's secret was safe with her.
In "A Friend in Need" we can see Adam fall out of a flying skycar in the middle of downtown Eternia, and no one one seemed to notice it; no one must have been looking out of their window that day.
Attack trak must have known, he changes in front of his talking trak all the time.
The animation shows He-man always changing in front of the castle, so it could be argued that no one sees the transformation, because he is sent to Greyskull and sent back as He-man, but this is wrong, because the cartoon shows the lightning traveling great distances to get to him.
In at least one She-ra episode ("Swifty's Baby"), another character from the ones that knew the secret (in the opening credits) knew that to get the sword to do something, one must say " for the honor of gray skull".
The magic of Grayskull is so powerful that when Adam calls upon it to transform into He-Man, it covers him with it such that nobody can see that He-Man and Adam are in fact the same person. The power of Grayskull makes people see someone else, not Adam.
