This is a Comon Female Blade but when she is summoned by you she seems to be missing her shoes so could she be  broken Blade or a Uncommon one for been barefoot by default?

She doesn't have a name as that is your choice and her personality varies just like how Common Blades may look the same but different.

She is very loyal as you are her Driver *Master* and  will assist you in battles and any task you wish for her to help you with.

She isn't weired or freaked out that she is barefoot though