If I understand you correctly, it should be...
?> <a href = edit.php?name=<?php echo $user ?>>Modify one of my contacts</a>
If you'll notice the majority of it is written in html rather than php... you close the php script at the beginning, begin the html hyperlink, then when you need to input the variable you begin a new php script have it return the variable $user, Close that php script, close the A tag, type in the text to be displayed as the hyperlink and end the hyperlink.
i just woke up, so I hope i'm right
😃