It is the highest river in terms of elevation

1. Indravati, 
2. Sun Kosi, 
3. Tama Kosi, 
4. Likhu Kosi, 
5. Dudh Kosi, 
6. Arun Kosi, and 
7. Tamar Kosi are the seven streams that form the Saptakosi. Eventually, it’s just called the Kosi.

https://www.google.com/search?q=koshi

In mythological times, the Kosi was called Kaushiki. Brahma had a Kusha and Gadhi was his grandson Description: Richikawho had a daughter Satyavathi.

The venerated sage, Richika asked to marry Satyavathi. Gadhi was not agreeable to the young and beautiful Satyavathi marrying the much older Richika. So, he asked Richika to bring a dowry of one thousand white horses each with one black ear, assuming it would be impossible for the old Brahmin to do it.

But, Richika immediately went to Varuna for help and got his thousand horses, which he promptly presented to Gadhi and married Satyavathi.

http://powerwarrior.blogspot.com/search/label/Ancestors

There came a point when both she and her mother wanted sons. Satyavathi wanted a learned son and her mother wanted a son with warrior traits. Richika being a powerful sage prepared two bowls of magical porridge, one for Satyavathi and one for her mother.

The mother assumed the sage would have prepared a more powerful porridge for his wife Satyavathi. She persuaded her daughter to exchange the bowls. When Richika heard this, he was furious, for now Satyavathi would bear a warrior. When she begged him to set it right, he said her grandson would bear the warrior traits, not her son.

And so it happened that Satyavathi bore Jamadagni, a scholarly sage, whose son was the ferocious Parashurama. Her mother bore Vishwamitra, who was initially a powerful king but then went on to become a powerful sage. As Vishwamitra was born in the dynasty of Kusha, Vishwamitra was also called Kaushika and his sister was Kaushiki.

http://powerwarrior.blogspot.com/search/label/ParashuramVishwamitra

Over time, Richika died and went to heaven and Satyavathi too followed him there. This Satyavathi, who was also called Kaushiki, is the river which descended on Earth as the river Kaushiki. The name over time morphed to Kosika and then Kosi. Even today, there are many old folksongs in which Kosika is used.

In times of legends, a demon asked the beautiful Kosi to be his bride. She agreed, provided he could contain her within the Himalayas by morning. The demon slogged through the night and to Kosi it appeared like he would succeed. Worried, she took Shiva her father’s help. Shiva disguised himself as a rooster and crowed a little just before dawn. The demon thought he had lost and went away, leaving the Kosi free to flow where her heart took her.

https://freeglobaluniversity.blogspot.com/search/label/ShivaDurgaSkandaGaneshaAgastyaVyasaEarthMosesBuddhaChristMuhammadKabirSai

Source
http://teachersofindia.org/en/article/story-river-kosi