Why chant "Hare Krishna" and not other names of God?
Devotees of Krishna chant many different names of the Supreme Person. Many Vaishnava songs are composed exclusively of names of Krishna representing His different pastimes. We also chant different names of Krishna during daily temple worship.
However, Chaitanya Mahaprabhu specifically recommended the maha-mantra—Hare Krishna, Hare Krishna, Krishna, Krishna, Hare Hare , Hare Rama, Hare Rama, Rama Rama, Hare Hare—as the most potent names particularly recommended for this age.
Srila Prabhuapda comments:
"The Supreme Personality of Godhead has many names, which are all non-different from the Supreme Person. This is spiritual existence. By chanting the Hare Krishna maha-mantra, consisting of names of the Supreme Lord, we find that the name has all the potencies of the person.
The Lord's activities are many, and according to His activities He has many names. He appeared as the son of Mother Yasoda, and also as the son of mother Devaki, and therefore He is named Devaki-nandana and Yasoda-nandana.
Parasya shaktir vividhaiva sruyate. The Lord has a multitude of energies, and therefore He acts in multifarious ways. Yet He has a particular name. The sastras recommend which names we should chant, such as Hare Krishna, Hare Krishna Krishna Krishna, Hare Hare. It is not that we have to search for some name or manufacture one. Rather, we must follow the saintly persons and the sastras in chanting His holy name." (Srimad-Bhagavatam, 8:1:13 Purport)
The song "Jaya Radha Madhava," which devotees chant daily before reading the Srimad-Bhagavatam, is also composed of several wonderful names of Krishna, and so is Om Namah Bhagavate Vasudevaya. Actually there are so many it is impossible to enumerate here.
I hope this is helpful.