Is each of Vishnu's 1000 names from the sahasranama of equal potency?

Question

I think some Purana says saying Rama's name 3 times is equivalent to reciting the entire Sahasranama. The Hare Krishnas also have a similar claim regarding the "hare krishna" mantra. There is a Puranic story that saying "narayana" on your death-bed grants you liberation, regardless of however many sins you have committed.

As far as I know, only these three names have been singled out this way. Is that correct?

Answer 1

In Padma Puraana, Uttarakhanda, Chapter 71

महादेव उवाच ।
राम रामेति रामेति रमे रामे मनोरमे ।
सहस्रनाम तत्तुल्यं रामनाम वरानने ॥ ३३१॥

Shiva said-
ShreeRaama, Raama, Raama , this itself merges(Rama) one in Raama who is beautiful faced and pleasing to mind.
This Raama naama is equivalent to SahasraNaama of Vishnu.

So Raama naama is most powerful Maheshvara Shiva himself has said it.

Thanks @Tezz for providing correct reference.