Get all file names (just the basenames) in a directory.

filenames.sh

#!/bin/bash

# Get all files in the folder.
FOLDER=/path/to/my/folder/*

# We'll build the list of file names here:
FILES=()

# Add just the basename of each FILE to the list of $FILES.
for FILE in $FOLDER
do
    FILENAME=$(basename "$FILE")
    FILES=( ${FILES[@]} $FILENAME )
done