That would depend on the type of direct deposit that is being made.
If the direct deposit is from a paycheck then you should be able to get the money direct deposited into the other persons bank account as long as you have their information and contact the bank and have the person say the direct deposit going into their account is okay.
If it's an IRS direct deposit then most likely the bank will reject the deposit since the names don't match.
If you don't have or can't get a traditional bank account you might look into getting an online bank account such as chimebank or any of the others to have your money direct deposited into instead.
There's also the bluebird American Express debit card you can get through Walmart or bluebird.com and you can have your money direct deposited into the account for no extra charge.