Bear in mind there's a chance they'll think you've joined some kind of suicide cult and that was the primary motivator for the suicide. If it's important for you that they learn your motives, mentioning the site could obfuscate them.
Yep.
You can absolutely mention the site, but it may end up being a quote in the next article about this site, and every article is a "Suicide is bad, this site exists, therefore the site is bad" article. They always imply the deceased would be alive, happy, and carefree, YOLOing on Insta while taking anti-depressants if only they hadn't accidentally clicked on the evil SaSU link by mistake. Every. Single. Article.
"My child, who had the name on this site of 'blowingmyheadoffsoon' was such a happy good boy, who never was sad, and always loved fun. I don't know how he accidentally got there, but clearly the site did something to him to change him and that's why this has happened. Please stop this evil site. If only it hadn't existed, he would have gotten the help he needed and opened up to someone who cared"
Then add like 20 more paragraphs about how SaSu makes jesus upset and lawmakers need to ban the internet to stop suicide and you have yourself a typical award winning BBC article.
It's not the parents fault when they are angry at this site because it's normal to be angry when you lose someone and to blame others. But yeah, if you make this site a big part of your suicide note, it's much more likely there will be an article about this site shortly thereafter.
It also will not matter if you've been depressed for years, have previous suicide attempts, or were taking anti-depressants for a while or had a therapist; it will not even matter if you literally put in your suicide note "I was planning to ctb before knowing about SaSu and would have done it anyway": if you die and mention SaSu in the note, there will be 1 and only 1 clear cause of your death: SaSu (according to the BBC or some other new organization).
They will also show a picture of you in the article possibly, and you will look extremely happy, be wearing bright fun colors, and look sort of care-free and clueless, like the type of person who genuinely could type into google "How do I make my brownies extra sweet?" and then accidentally click on a SaSu link that took you to a post about methods, because the photo will make you look that happy, innocent, and clueless.
But it's your note, do whatever you want (except random plug for my "pro-life" post about not ctbing that everyone hates... called "things to do prior...") I think it will be distracting and lead your family into some labarinthian maze like attempt to place blame instead of just grieving normally. They probably would want to know everything, but if they do, it really could end up as an article.