Anything that you configure in your mappings does not change the actual documents. It only changes how Elasticsearch will treat the documents. So, none of it impacts the _source that Elasticsearch returns.
In your example, Elasticsearch will create an inverted index for a field full_name and it will copy the values of name.first and name.last to that inverted index, so you can query that field, even though that field does not actually exist in your document. You can think of full_name as a "virtual field". For example, the following query works as a result of your dynamic template:
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