You mean the title only as seen in the tiddler head? You'd just restrict it by targetting .tc-titlebar or whatever the class is.
I am actually working on another variant but I don't get it to work properly;
LinkAlias This
hides the title link where it appears and only shows the :before attribute with content fetched from the alias field. I.e it "exchanges" the title for an alias. It is simple to have it work for only the tiddler title but to have it work for every place where the title appears is problematic as you can see in the link. The technique to hide the original name can, as far as I know, ony be achieved with visibility:hidden or font-size:0 ....but this of course also affects the :before style (i.e the alias) so this has unintended consequences.