When Shree Krishna is with the ‘middle’ Pandava - Arjuna, who is the incarnation of Lord Nara, they should be known as NaraNarayana. Bhaarat explains: Arjune Tu Naraveshaha Krushno Narayana Swayam - ‘Arjuna is the incarnation of Nara and Krishna is Narayana.’ Similarly the Bhagwat explains, ‘The two of you are the Rishis Nara and Narayana.’
In the same way, he can be known as Rama-Krishna, Satya-Krishna etc. when accompanied by Balbhadra (Balarama), Satyabhama and others.
Just to clarify, Nara-Narayan are famed as ‘Bharat Khanda Na Raja’ - the Lords or Kings of the Earth, who are continuously performing penance in Badrikashram for the benefit of mankind. They were born of Murti Devi and Dharma Prajapati.