You need to understand how it works.
#ANCHOR will look in source code of the page for element with ID ANCHOR and scroll to it, so If You would like to change name of the anchor, You would need to either edit template core layout files, or modify the way joomla generates the ID's of the elements. While first solution is less or more easy to do (while changing the ID's You also need to correct all CSS files), the second one is quite impossible to do.
So as long as You use ID's that are provided automatically You can add/remove or relink almost anything in menu, if You would like to change ID's of elements - now You know why there is no solution for that.
But there is an idea that comes into my mind. For elements that are entered with use of customHTML module, You can place empty div in the beginning of that module for example:
<div id="myAnchor"> </div>
and link to it with use of #myAnchor