Depends on the country, but usually a “background check” is nothing more than paying a lawyer to check if you have ever been convicted, accused or investigated for a crime. Prosecutors have an archive and a office of records to collect and share that public information. This is why clearing records are important in courts and settlements. It’s a big mark to say the person is actually alright and won’t be found in the records if searched, as they were cleared. Other than that it is usually just a phone call to a previous employer to ask if you were an asshole there.

Related: A very similar question posted by the same person yesterday.

Unless they ask you for your reddit/lemmy account during the background check process and you willingly give it, I imagine they only go as far as checking social media accounts that are searchable with your known names, email addresses, and phone numbers on the major social media platforms. That’s if you keep your lemmy account relatively anonymous of course.

Why do you ask?

I am not sure if by any chance they do the extra mile to check on that. However, as a rule of thumb you should try to keep private stuff away from work stuff, meaning, at work maybe is not the best idea to boast about your reddit profile where you happen to follow some nsfw stuff (or other stuff that can be considered offensive and/or can lead to controversy). I would imagine they try to check things such as accounts attached to an email or phone number (for instance). If a set of aliases were used for this (or different info) from your work email phone etc., you should be able to keep it separate.