Name change or DBA?
As you correctly defined in your question there are two ways to rename the business: one is to completely amend the business name, and another is to register a DBA for the company, this way maintaining two (or more) names for the business.
Even though both approaches will achieve what you are after I would say adding a DBA is somewhat less disruptive for the business than amending the Articles of Incorporation/Organization. After adding a DBA all you would need to do is to notify your bank of the new name so that your bank account would have the DBA on file in case you get payments to the new name, and thats about it.
With name amendment you would have to change the name of the company everywhere (for example notify the IRS about the change), so its a bit more of a headache.