Solution is not to use the batch tool! In my opinion it's a clunky interface that existed prior to model builder iterators but has persisted for a variety of reasons. As you see you are hitting the limitations of this interface. A very simple model using a FeatureClass iterator with inline variable substitution to help you create your unique names is the way to go. Getting your head around iterators will unlock all sorts of potential for mass automation.
Don't know model builder? Try reading the walk throughs in the help file or get yourself on a training course.
Setting up the model will take less than 2 minutes, running, well that's down to machine/network performance.
I hope you have learnt that next time write your questions with more detail and as you see you get quick answers!