Novel where the MC is well-known for being lazy or the MC have secret Identity and it get gradually reveal along the story. Other than this point, I don't mind other things. The one that I've read, Ma'am you've been uncovered and Rebirth of idle noblewoman
The Silly Alchemist - A story where basically a person transmigrates to a new world (like usual), though into the body of a child. Normally children novels are horrible, though this novel actually makes it readable, and actually make turn the point into a positive. Basically his special power is absolute dumb luck. He is the luckiest person in the world, and nothing unlucky will ever happen to him, though this power is not 'tangible', and you just accept that he is lucky. Another point is that he wants to be a parodical son with a dream to bankrupt his family. However, the constant conflict of interest is that he is never able get even one dime in the negatives due to his luck. Buy a random wooden box for the price of a city, its a guide to alchemy worth a county. Buy a useless mountain? Military grade ore is discovered within a week. And thus the story continues... The story is more on the comedic light hearted side which is decently rare among novels I've seen, so I would highly recommend it.
Maybe: The Strongest Dull Prince’s Secret Battle for the Throne Tensei Shite Inaka de Slowlife wo Okuritai Previous Life was Sword Emperor. This Life is Trash Prince Jitsu wa Ore, Saikyou deshita?
my family's idol's vest fell again but the MC isn't exactly lazy he's just not bothered to reveal his identities
Sign-in Buddha’s Palm it has a low key protagonist who was a weak handyman disciple at first but later became op. At first people don't know his identity and it is later revealed slowly. The later arcs also have some points relevant to what you asked in this post. Also try 'lazy MC' in the tags and you can also search for it in the forums search.
MC wants to do nothing but sleep. He is powerful because he does nothing but sleeep https://www.novelupdates.com/series/the-lazy-king/