Question
Why is God’s name used for people?
Answer
One of the primary reasons is the sin destroying effects the Lord's names. The inspiration for doing this can be linked to the story of Ajamila as described in the Bhagavatam:
Ajamila was a pious brahmana. But once he saw a prostitute engaged with a man in the forest and since then he got infatuated. He fell down from his religious activities and went so low as to marry the prostitute herself. He abandoned spiritual activities and engaged in sinful ones. In course of time he begot ten sons from his wife and he had named the youngest one who he loved very much as Narayana. At the time of his death when the minions of Yama came, out of fear he repeatedly called his youngest son with his name Narayana. As he took the name of the Lord, messengers of Vishnu came and realised him from the fetters of Yama. Vishnu dootas discussed with the Yama dootas why he shouldn't be punished. Hearing this conversation, Ajamila could know his mistakes and got back his life. Then he spent rest of his life practising devotion to the Lord and finally went to Vishnu's abode after his death.
So even the holy name of the Lord is powerful enough to redeem people of their sins. Hence, Yama said to his messengers the importance of chanting Lord's name as below:
Therefore it should be understood that one is easily relieved from all sinful reactions by chanting the holy name of the Lord and chanting of His qualities and activities. This is the only process recommended for relief from sinful reactions. Even if one chants the holy name of the Lord with improper pronunciation, he will achieve relief from material bondage if he chants without offenses. Ajāmila, for example, was extremely sinful, but while dying he merely chanted the holy name, and although calling his son, he achieved complete liberation because he remembered the name of Nārāyaṇa. [SB - 6.3.24]
My dear servants, please bring to me only those sinful persons who do not use their tongues to chant the holy name and qualities of Kṛṣṇa, whose hearts do not remember the lotus feet of Kṛṣṇa even once, and whose heads do not bow down even once before Lord Kṛṣṇa. Send me those who do not perform their duties toward Viṣṇu, which are the only duties in human life. Please bring me all such fools and rascals. [SB - 6.3.29]
Due to this effect of God's name, people in India generally name their children such.
Reference:
Shrimad Bhagavatam, Canto 6, Chapters 1-3
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