I know of oxyhaemoglobin but the mixture of plasma and haemoglobin in the blood gives what?
You and Dr. James must be friends ;)
There is no specific name for the mixture of plasma and haemoglobin, however, when hemoglobin is found in the plasma (i.e. not in blood cells) it is usually referred to as "free hemoglobin." This is a term you are most likely to encounter when dealing with plasma/ serum hemoglobin testing.
Additionally, when haemoglobin is broken down, it forms bilirubin, which contributes to the color of plasma (there is no specific name for the mixture of bilirubin and plasma either, except perhaps "plasma bilirubin").