Backgroud checks are a direct expense, but I don't want to code legal and professional expense because some professional expenses are not part of the direct expenses.
What should I code background checks

I can't verify whether something is direct or indirect cause I don't know what your company is doing.

Unless there's something special here going on that I wouldn't know about, I think this is very much opinion, though I'm not sure whether direct is relevant. I also want to make a point that I'm not sure if your use of the word "coding" is significant. I worked a place once where they called picking the account number "coding." However, that might be some industry-specific thing of which I'm unaware and my answer may not be appropriate for that. Keep that in mind. You might get more appropriate answers if we knew what industry it was.

I would normally call legal and professional expenses what is paid for, well, lawyers, and accountants, and that sort of thing. You can define "professional" any way you like. If you're paying an outside third party company to do the background checks, I could see including it.

I think it also depends on how much of your expenses that comprises. i.e. is it something done only occasionally that not much is spent on? Then it's easier to lump it in with something else or even into miscellaneous. (I dislike using miscellaneous unless it's a very immaterial amount and really just doesn't belong elsewhere.) If it's a fairly material amount, you can always separate it out as its own expense, or lump it together with some other similar expenses.