I suppose it was Nojiko who gave them their names in the initial version of game when she was their mom. After a series of rework it turned out that she adopted them at the age of three.
We all know why is that, but hush 
So, right now it would be a little bit difficult to explain why she gave them their names, but it's not impossible! After all we have learned to ignore the "why she is red" question.
Or maybe Nika is an anagram for Kain, and that explains some of his character traits. Or maybe Nika went crazy after his parents died and made up an imaginary girl named Summer for himself, but in fact Nami was with him when he hallucinated that he was with Summer. Cause she didn't want him to be put into a nuthouse. And she helped him to believe that this delusion about Summer is gone, cause Nami is abbreviation for National Alliance on Mental Illness.
But I prefer to think that their names are what they are, because if they were called John and Jane, it would be a bit boring (With all due respect to every John and every Jane).