Currently batch renaming relies on Blender to number duplicates.
Numbering could be supported:
Example: a chain of finger bones. These would usually be named Index.01.L, Index.02.L, Index.03.L and so forth.
For numbering to work usefully we would want a way to sort items before they're numbered (by their current alphabetical order, hierarchy, location... possibly others).
This needs some design to think of how to expose this to users usefully, see suggestion: rBa5b1231de790#244815