Well, it looks like you really can't change this. In customer defaults or preferences, you can change the font, thickness and the color.
So, my next try was creating a macro. With Tools/Macro, I have recorded a macro, that always opens IdentificationSymbol dialog box and uses Square shape instead of circular. I have already tried tis macro and it works fine on my computer.
I have attached the macro here on this post. Please let me know, if it is working for you.
REgards.