As per the original Vishnu Sahasranamam as detailed in Anushasana Parva of Mahabharata, names like Gopal, Rama and Govinda are mentioned for Lord Krishna/Vishnu, but not Kanha/Kanhaiya. So, from which scripture, the names Kanha/Kanhaiya came from when they are not in Vishnu Sahasranamam?
The Pali Text Society's Pali-English Dictionary has the following meaning:
Kanha (adj.) [cp. Vedic kṛṣṇa, Lith. kérszas] dark, black, as attr. of darkness, opposed to light, syn. with kāḷa (q. v. for etym.); opp. sukka. In general it is hard to separate the lit. and fig. meanings, an ethical implication is to be found in nearly all cases (except 1.). The contrast with sukka (brightness) goes through all applications, with ref. to light as well as quality...
Just as Kṛṣṇa and Kṛṣṇā are used in the Mahābhārata to refer to Kṛṣṇa (s/o of Vāsudeva) and Draupadī, the Buddhist Jātaka tales use Kaṇha and Kaṇhā in a similar way. From Dictionary of Pāli Proper Names by G. P. Malalasekera:
3. Kaṇha.–Another name of Vāsudeva (J.iv.84, 86; vi.421; PvA. 94 ff.); the scholiast explains that he belonged to the Kaṇhāyanagotta.
4. Kaṇha.–Son of Disā, a slave girl of Okkāka [Ikṣvāku]. He was called Kaṇha because he was black and, like a devil (kaṇha), spoke as soon as he was born. He was the ancestor of the Kaṇhāyanagotta (D.i.93). Later he went into the Dekkhan and, having learnt mystic verses, became a mighty seer. Coming back to Okkāka, Kaṇha demanded the hand of the king's daughter Maddarūpī. At first the request was indignantly refused, but when Kaṇha displayed his supernatural powers he gained the princess. D.i.96f.; DA.i.266.
1. Kanhā.–Daughter of the king of Kosala. Before she was born, Brahmadatta, king of Benares, killed her father and carried off her mother. When the child was born, Brahmadatta adopted her as his own daughter; she is, therefore, called dvepitikā (=having two fathers). The king promised to grant her a boon, and she held a svayaṃvara, at which she chose as her husbands all the five sons of King Paṇḍu; Ajjuna, Bhīma, Nakula, Yuddhitthila, and Sahadeva. (According to the Mahābhārata, Draupadī, daughter of the Pañcāla king, was the wife of these five princes.)
By her strong passions she won the love of them all. Not satisfied with them, she also made love to a hump-backed slave who was in her service. One day, when she was sick, all her husbands were gathered round her, and she made signs to each of them to show that she loved him best. Ajjuna, however, was suspicious, and by questioning the hump-back, learnt the truth. The five brothers left her and retired to the Himālaya, where they became ascetics. The story was related by Kunāla, who is identified with Ajjuna. (J.v.424, 426f.)