When right-clicking on a symbol and choosing "Refactor VAX -> Rename", or pressing Shift+Alt+R on a symbol, have the popup UI's input box caret located at the same spot from where the event was triggered.
int foo(int bad|name);
The caret is there between "d" and "n" in badname. When triggered, the UI should pop up with the caret also there. In addition, if a portion of the symbol had been selected (such as highlighting "n" in "badname" (to change it to "N"), then also select the same range in the UI popup.
Interesting idea. Currently rename selects the whole word, so you can easily type a new one, which is usually convenient: just type the new name without caring about the current one, it just gets replaced. Editboxes tend to select the whole word when they get the focus so it's also consistent with this practice.