Can a standard function access the name its been given?

e.g can I access the name as a variable inside the function?

yes you can actually, it's listed on the "writing functions" doc page:
node.name
https://nodered.org/docs/user-guide/writing-functions#node

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Now, if only there was a built-in property for node.outputs (how many output ports are defined)...
or better yet, an array of output definitions (with labels and such).

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