Usually whales are in a form of institution but if it's a single person, I think they buy bitcoin via OTC or over-the-counter. They find someone who sells bitcoin in their area then meet each other to do the trade.They don't go through to decentralized exchanges to buy because these DEXs' will definitely ask for some documents to withdraw that huge amount. It will also create a sudden pump on lower timeframes if they buy directly on those exchanges.
But there is a situation when very large volumes appear on the CEX for certain coins, is it not whales, ofcorse the exchange itself can to do this. I think there are different whales, someone prefers complete anonymity, someone can be verified and work openly. In my understanding, whales are the same people as us, just a little smarter, a little more discipline, someone is more fortunate, but otherwise we are all people.