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?