Replace document name

How could I replace a open document name with a new name?

I have a script that creates the new name but I can't figure out how to send the new name back to photoshop replacing the open document name.

Here is the current script:

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layerN = activeDocument.activeLayer.name

var doc = app.activeDocument

var fname = doc.name.split(".")

var fname = fname[0]

var newDoc = doc.duplicate(fname+layerN,true)

//var newDoc = (fname+layerN,true)

app.activeDocument.name = newDoc

newDoc.flatten();

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Right now this one makes a duplicate of the original document with the document name like I want, but I would rather just rename the original document instead of making a duplicate.

Any help is appreciated.