Batch alignment of inconsistently named Fastq files
A very simple approach, but one which will work with the names you show, is to remove any occurrence of 00N (where N is any number) from right before the .gz. To do so, edit your script to:

for i in $(ls *.fastq*.gz | sed 's/00[0-9]\.gz/.gz/' | rev | cut -c 16- | rev | uniq); do 
  bowtie2 -q -p20 -x /run/media/punit/data1/BowtieIndex/hg38 \
    -1 ${i}R1_001.fastq.gz \
    -2 ${i}R2_001.fastq.gz | 
        samtools view -bS - &gt;${i%}.bam"
done