The username is being stored properly.
You were using code to display it:
echo $_SESSION['SecurityAssist_username'] > "<br />";
Which is displaying whether the value is greater than "<br />", which is doing an alphanumeric comparison and returning "1" for true.
Updating that line to:
echo $_SESSION['SecurityAssist_username'] . "<br />";
displays the username with the br tag appended.
Yes, you can just change the save as field name to whatever you want either in the code on the login page or through the UI.