How do stock trading companies pay tax?

I was trying to understand the business structure of stock trading companies.

They're called brokerages, and they earn money in one of four ways:

1. by "skimming" a little bit off the top of each person's account,
2. charging a transaction fee, or
3. both.

When you trade (buy and sell stocks) in the name of another person , how do you show that the profit/loss should be directed to the person who was buying the stocks and not the LLC?

You keep separate account of each person's money, and then pass their capital gains, losses, dividends, interest, etc through to them.

It's little different from your bank savings account statement (and thus year-end 1099) showing how much interest you earned.

Is there any document which you need to file? What happens if the person buying the stock is anonymous in bitcoin exchanges?

The SEC does not allow that. A company named Abra seems to think it has found a way around that by not actually buying shares in the investor's name, but you still have to keep account of each individual investor's investments.