Is it possible to rename a survey "after" it has been "sent"?

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Is it possible to rename a survey "after" it has been "sent"?

There are a few surveys that were named incorrectly while sending so to avoid confusion in future, we would like to rename some of the surveys.

I see that every survey is sent, a document is created.

Question: We would like the "updated" survey name to show up in customer's record. Is it possible? 

On test site, I renamed the document and the custom record does show updated document name. But, even when I rename the actual survey name, the old survey name show up in customer's record "Marketing Tab".