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Interesting question, impressive code.

I only found one thing that could be considered a bug: nameNumber('15.000') will return "one hundred fiftyundefined thousand", this could be fixed by changing your regex to

if (!number.match(/^(-?)[\d,]+$/)) {
    throw new Error('invalid number: ' + number);
}

Other than that I think you went a little overboard in some places to achieve the ultimate DRYness.

This:

var digits = ['', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine'];
var tens = ['', 'ten', 'twenty', 'thirty', 'forty', 'fifty', 'sixty', 'seventy', 'eighty', 'ninety'];
var teens = { 0: 'ten', 1: 'eleven', 2: 'twelve', 3: 'thirteen', 5: 'fifteen', 8: 'eighteen' };

function nameDigit(digit) {
    return digits[digit];
}

function nameTenToNineteen(number) {
    return teens[number] || digits[number] + 'teen';
}

(ignore the removed newlines) puts the 'teen' back in the teens array, you no longer need a temporary variable or encode that you do not have the add 'teen' for 10,11 and 12. This has less characters, and less complexity.

The same ( though I am not sure this would reduce character count here ) can be said for scalePrefix, it took me a while to figure that this was supposed to return milllion, billion etc. If you were to add '', 'thousand' and 'illion' at the end of existing entries, then your nameTripletScale could be

function nameTripletScale(digitCount) {
    return scalePrefix[digitCount / 3 ];
}

Note how it sneakily removes an offensive ternary :P It would also no longer require the magical +2 in if (digitCount / 3 > scalePrefix.length + 2) {

In extractSymbols you mix parsing, conversion, validation and error handling, I usually don't like that but the code is succinct enough that I can not offer a reasonable alternative.

The same goes for function append(item) { in nameNumber, it looks a bit busy but removing it looks worse.

One last item is nameDigit(digit), it requires more characters than say digits[digit] and about half of the time you actually use direct array access instead of calling nameDigit, I would just drop nameDigit entirely.