Can you spell koi as c-o-y in the fish and is it an abbreviation?

No, the word "koi" is not spelled "c-o-y" and it is not an abbreviation.

* Koi is a Japanese word that refers to a type of domesticated carp. It is spelled k-o-i.

* Coy is a separate word that means shy or reserved. It is spelled c-o-y.

There's no connection between the two words, and "coy" is not an abbreviation for "koi".