You cannot delete your account.
One of our users writes:
“Hacker News (HN) does not have a way to delete your account, but you can ‘anonymize’ your profile. [read the tip below!]. If you used your real life name as your username it’s a bit more of a problem, especially if your name is not ‘John Smith’, you could try emailing the owner of the site either at email@example.com or firstname.lastname@example.org. […] From my experience you can email email@example.com and ask to make your account inactive but they won’t delete any posts or submissions that you have made as I’ve been told ‘they are just too entrenched’.”