In bash, how can I echo the variable name, not the variable value?

If you want to simply output a static variable name, you can escape the $-sign:

echo \$var

The shell parameter expansion ${!name@} or ${!name*} could do the trick,

$ foo=bar
$ var_name=(${!foo@})
$ echo $var_name" = "$foo
foo = bar

Although feasible I can't imagine the utility of this ...