Write a program called valid that prints yes if its argument is a legal shell variable name and no otherwise:

$ valid foo_bar
yes
$ valid 123
no

if [ $# -ne 1 ] ; then
echo "Error: no variable name to test"
exit 1
fi

if [ -n "$(echo $1 | grep -E '^[a-zA-Z][a-zA-Z0-9_]{0,}$')" ] ; then
echo "yes"
else
echo "no"
fi

Note this works because the regular expression defines the valid language of a shell variable as an upper or lower case letter followed by zero or more alphanumeric values or an underscore. To work properly note you also need to use ^ to left root the expression to the beginning of the word and use $ to get the end of the expression, making sure the entire word given meets the regular expression's rules.