The correct name is कृष्ण with ण.
The problem in pronunciation is due to the mistake in transliteration from Sanskrit to English. Now a days, the letter 'ऋ' is written as 'ri' and pronounced as 'रि' which is wrong. Same applies to ऋग्वेद which is now written as Rig Veda. Its transliteration according to IAST is Ṛgveda. Same for 'ऋषि' whose transliteration is Ṛṣi according to IAST.
To overcome this problem, different transliteration schemes like ITRANS , IAST, Harward Kyoto have been designed. Using one of those transliteration schemes would solve the problem. (IAST has an advantage over other as capital letters are also allowed in it. Other transliteration schemes don't have capital letters. Using capital letters is wrong transliteration according to other schemes.)
It is written as कृष्ण in all the scriptures.
इन्द्रस् तदात्मनः पूजां विज्ञाय विहतां नृप
गोपेभ्यः कृष्णनाथेभ्यो नन्दादिभ्यश् चुकोप ह
Indras tadātmanaḥ pūjāṁ vijñāya vihatāṁ nṛpa
gopebhyaḥ kṛṣṇa-nāthebhyo nandādibhyaś cukopa ha
Śukadeva Gosvāmī said: My dear King Parīkṣit, when Indra understood that his sacrifice had been put aside, he became furious with Nanda Mahārāja and the other cowherd men, who were accepting Kṛṣṇa as their Lord.