To use your Daniel Day-Lewis example, it’s as if people referred to him as “Daniel Michael Blake” when trying to sound familiar or as “Day-Lewis” when trying to sound more formal/neutral/maybe adversarial. But, unlike with Daniel Day-Lewis, pretty much no one in Mexico knows about AMLO without also knowing his full (two given names, two surnames) name.
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I agree, it is rather uncommon that he is known for several combinations of his name. He has been a public figure in Mexico for a couple of decades now so I think that’s part of the problem. I believe he actually campaigned (and I know some of the official government announcements use it) as “Andrés Manuel” since it’s more familiar.