In 2010, you came across a site that was giving away bitcoins. The site said it was free money so you signed up. You were logging in to figure out how it was money but couldn't. The last time you logged in you had more than 100 bitcoins. Later you forgot about the site until 2017 when a ponzi was advertising Bitcoin. Bitcoin? The name rang a bell and you stated hearing stories. You remembered you must have many bitcoins somewhere but you can't even remember the name of the site. How would you recover your BTC?
Name of the website doesn't matter in any way. According to what you said (in imaginary) you had bitcoins on website's account which are just numbers before withdraw.
All you can do is search for websites and if you really search, you may find url and then put that url on web.archive.org and the best you can do is to find website's contact page (email of owner) but more likely it will be email with domain's name and even your attempt to contact owner will fail. Even if you contact, what do you think, will he give a f*** to what you say?
To make it easier for you, you can't make person from dead to alive, so the same applies to your bitcoins.