I would not advise just collecting all files that match *.mp3 and then trimming the file names. You MAY want to run this same script AGAIN later (like next week) and it should NOT try to rename the same files a second time, making them even shorter and have naming conflicts.
Your example file names seem to be 001xyz1.mp3 and you want xyz.mp3
KEEP_DIR=$PWD
cd /your/music/base_dir # sub-dirs holding .mp3
RCOUNT=0 ; SKIP=0 ; FCC=0
for FFF in */001???1.mp3
do
LOC="$(dirname $FFF)"
BAS="$(basename $FFF)"
TRIM1="${BAS#1.mp3}" #could use ${BAS:4:3}
NEWF="$LOC/${TRIM1%001}.mp3"
if [ -e "$NEWF" ] ; then
echo "#-- File $NEWF already exists, not renaming $FFF"
SKIP=$((SKIP+1))
else
mv $FFF $NEWF
MCOUNT=$((MCOUNT+1))
fi
FCC=$((FCC+1))
done
echo "Renamed $MCOUNT mp3 files, of $FCC found. (Skipped $SKIP)"
cd $KEEP_DIR
#--[eof]