Since your file names contain spaces the for loop won't work as is.
Once you have a list of file names, a test on the number of files matching y*.pdf
to determine if you need to merge the pdfs.
#!/bin/bash
LIST=( * )
# Remove .pdf extension. merge pdfs. delete originals.
for x in "${LIST[@]}" ; do
y=${x%%.pdf}
if [ $(ls "$y"*.pdf 2>/dev/null | wc -l ) -gt 1 ]; then
pdftk "$y"*.pdf cat output "$y"_merged.pdf
find "$y"*.pdf -type f ! -iname "*_merged.pdf" -delete
fi
done