Regular Expression problem

[shogun1234]

I have a string which looks like

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LIST(NAME(john,123),NAME(brown, 456),...)

In vim I want to wrap personal names with double quotes. So the string would become

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LIST(NAME("john", 123), NAME("brown", 456), ...)

The RE I attempt to match is

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:g/NAME\([:alpha:],\d\)/s//NAME\(\"\1\",\d\)/g

But I find I can't match personal names. What's the write way to match personal names with RE? Vim version is 8.1. Thanks