How to determine function name from inside a function

You can use ${FUNCNAME[0]} in bash to get the function name.

From the Bash Reference Manual:

FUNCNAME

An array variable containing the names of all shell functions currently in the execution call stack. The element with index 0 is the name of any currently-executing shell function. The bottom-most element (the one with the highest index) is "main". This variable exists only when a shell function is executing. Assignments to FUNCNAME have no effect and return an error status. If FUNCNAME is unset, it loses its special properties, even if it is subsequently reset.

This variable can be used with BASH_LINENO and BASH_SOURCE. Each element of FUNCNAME has corresponding elements in BASH_LINENO and BASH_SOURCE to describe the call stack. For instance, ${FUNCNAME[$i]} was called from the file ${BASH_SOURCE[$i+1]} at line number ${BASH_LINENO[$i]}. The caller builtin displays the current call stack using this information.

When bash arrays are accessed without an index the first element of the array will be returned, so $FUNCNAME will work in simple cases to provide the name of the immediately current function, but it also contains all other functions in the call stack. For example:

# in a file "foobar"
function foo {
    echo foo
    echo "In function $FUNCNAME: FUNCNAME=${FUNCNAME[*]}" >&2
}

function foobar {
    echo "$(foo)bar"
    echo "In function $FUNCNAME: FUNCNAME=${FUNCNAME[*]}" >&2
}

foobar

Will output:

$ bash foobar
In function foo: FUNCNAME=foo foobar main
foobar
In function foobar: FUNCNAME=foobar main

I use ${FUNCNAME[0]} to print current function name