Rename "My Parts Bin"

You might try editing
My Documents\Fritzing\bins\my_parts.fzb
which looks to be xml and sets the bin name mine looks like this:

< ?xml version="1.0" encoding="UTF-8"?>
< module fritzingVersion="0.4.3b.0.0" icon="Mine.png" >
< title>My Parts
< instances>
< /module>

and I expect yours will have Adafruit Batteries in it. Be aware that bad things (including corrupting the whole mess, so have a backup) may occur

Peter