maybe you first create a table in the database. (e.g with 3 columns named 'name','password','user_name').
After however loging in in your system you could use php's session module/functions to register the username in the session.
Then you could on one page have a textarea filled with his name. (of course dynamically with php(could be: $sql = "SELECT name FROM users WHERE user_name = $sessionvar"😉 where $sessionvar could be the users user_name(you had stored it you database)).
So by now you have filled the textarea with the users real name. Maybe his username (user_name) is joe and his name (name) is Joe Goldenberg. So nw in the Textarea the value would be Joe Goldenberg.
The user (or admin or whatever you wanna do) can change this name and by pressing the submit button (<input type="submit" name="update" value="true">).
Now the main thing you were lokking for. The php-code to perform this update in a database (mysql maybe):
if($_POST/GET["update"] == "true"){
$sql = "UPDATE users SET name = '$textareaname' WHERE user_name = $sessionvar";
...
}
regards
ali