Since I know nothing about your code, I'll improvise.
1. In your login, you should have a user_id. ($_SESSION['user_id'])
2. In the database, the uploads table should have columns uploader_id.
When you upload the file, the query should contain:
$query = "INSERT INTO uploads SET uploaded_file = $file, uploader_id = $_SESSION['user_id'] ";
3. When printing out the upload, the query should have this:
$query = "SELECT uploaded_file_id, uploaded_file, username FROM uploads JOIN users ON uploads.uploader_id=users.user_id";
And then when you print out username, you'll get your user who uploaded the file.