Deleting your account removes your personal identity from Dugout. Your name, email, photo and login are gone. But if you hold a player record at any club, that record isn't deleted along with it: it's anonymised instead, renamed to something like "Former Player," while your stats and match appearances stay exactly as they were. That's deliberate. A hat-trick belongs to the other ten players' record of that match too, so removing the row itself would leave holes in leaderboards and season totals that were never yours alone to take with you.
The same ownership rules as leaving a club apply first, club by club, for anywhere you're the sole owner: you'll need to transfer ownership before deleting if other members are still there, and deleting will take the club with it if you're the sole owner and the only member left. The confirmation screen tells you exactly which club(s), if any, will be deleted alongside your account.