Well you are not supposed to change a built-in widget/module from Mysidia, it may have unexpected behaviors. Loginbar is an identifier used internally, so you shouldnt change it.
Anyway why do you want to rename it though? From a visitor's point of view, he/she doesnt see anything called 'loginbar'. You only see if if you are admin viewing the widgets/modules in ACP, and I dont know why this bothers you.