So if you’re going to make a genderswapped version of Batman, please consider naming her Bridget Wayne.
The name Bridget comes from the Irish goddess Brigid; while the wikipedia article on her definitely has some Neopaganism (TM) on it, this is what it says about her:
In Cath Maige Tuireadh, Bríg invents keening, a combination of weeping and singing, while mourning for her son Ruadán, after he is slain while fighting for the Fomorians. She is credited in the same passage with inventing a whistle used for night travel.
... She is the goddess of all things perceived to be of relatively high dimensions such as high-rising flames, highlands, hill-forts and upland areas; and of activities and states conceived as psychologically lofty and elevated, such as wisdom, excellence, perfection, high intelligence, poetic eloquence, craftsmanship (especially blacksmithing), healing ability, druidic knowledge and skill in warfare.
like come on you couldn’t get more thematically appropriate if you tried.