'ls -1' : how to list filenames without extension

ls -1 | sed -e 's/\.png$//'

The sed command removes (that is, it replaces with the empty string) any string .png found at the end of a filename.

The . is escaped as \. so that it is interpreted by sed as a literal . character rather than the regexp . (which means match any character). The $ is the end-of-line anchor, so it doesn't match .png in the middle of a filename.

You only need the shell for this job.

POSIXly:

for f in *.png; do
    printf '%s\n' "${f%.png}"
done

With zsh:

print -rl -- *.png(:r)

If you just want to use bash:

for i in *; do echo "${i%.png}"; done

You should reach for grep when trying to find matches, not for removing/substituting for that sed is more appropriate:

find . -maxdepth 1 -name "*.png"  | sed 's/\.png$//'

Once you decide you need to create some subdirectories to bring order in your PNG files you can easily change that to:

find . -name "*.png"  | sed 's/\.png$//'