Afterthough: the answer below is for medical devices, if your question is for non medical please ignore!
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There is a standard EN ISO/IEC 17050-1:2004 for the declaration of conformity (DoC), which requires that applied standards are shown on the DoC, but it is generic and not specific to the MDD.
It is a legal requirement in the MDD that you list the standards applied, although it does not say that you must include them in the DoC.
The MDD has a problem that there are a large number of harmonized standards that may apply to a single product (I have seen lists over a page long), so it is not practical to keep an accurate list in the DoC. As an MDD auditing over many years I never found a DoC with an accurate list of harmonised standards. Usually only a few high profile standards get a look in, and frequently the dates/amendments are wrong. Therefore, the issue of whether DoC's need to be updated & re-signed with every change of a standard is moot, while ever the standards shown are not accurate anyway.
An alternate method I have seen sometimes is to have the DoC declare compliance to the directive, and to avoid confusion, also provide a link to a separate document in the technical file which accurately lists all the standards applied including revision/amendment. I expect that as long as this list is updated, the DoC itself does not need to be re-signed with every design change, including new standards.