I think the strings for TheLoginInterface are loaded from somewhere you cannot edit. As recommended in an earlier post about text replacement in WebLink, one solution is to replace it using Javascript.

You can insert custom Javascript into the area above the closing body tag, </body>, in the Login.aspx file.

This worked for me:

<script type="text/javascript">
  var str = document.getElementById("TheLoginInterface").innerHTML; 
  var res = str.replace(/user name/i, "Your Replacement Words");
  document.getElementById("TheLoginInterface").innerHTML = res;
</script>

It looks for the "TheLoginInterface" element, then searches within that section for the string "user name" (case-insensitively, indicated by the /i ) and replaces the first instance it finds with "Your Replacement Words".