Answer: How to test if string exists in file with Bash? error handling in bash

grep -Fxq "$FILENAME" my_list.txt

The exit status is 0 (true) if the name was found, 1 (false) if not, so:

if grep -Fxq "$FILENAME" my_list.txt
then
    # code if found
else
    # code if not found
fi

Explanation

Here are the relevant sections of the man page for grep: