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This functionality exists within MAPublisher. You can do this by applying an expression to change the #Name column to equal the corresponding Postal Code value. To do this, open the MAP Attributes panel, click the Show/Hide columns button, then click Show All to reveal the #Name column which reveals the unnamed objects in your layer. Click Apply Expression at the bottom, apply it to the #Name column and click the Postal Code attribute field as your Expression. After clicking OK, the objects should be renamed in the Layers panel.
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Avenza Systems Inc.