What do you call the red pigment found in vertebrates that functions in oxygen transport?

There are actually two red pigments found in certain vertebrates that function in oxygen transport (or storage). Hemoglobin is present in the blood of most vertebrates and binds oxygen molecules, in order to transport them to body tissues in need of oxygen for energy (ATP) production.
Myoglobin, mainly in mammals, is a protein (enzyme) found in red (skeletal) muscle cells, that aids in binding oxygen when it's plentiful being delivered via blood. The purpose is that in high stress, low oxygen situations such as strenuous exercise, the myoglobin releases its bound oxygen to provide it to the starving overworked muscle cells.
**Fun fact: it's the hemoglobin that gives the bright red color of blood when it's bound to oxygen, and the myoglobin of mammal flesh gives it the typical pinkish-red hue that is seen in mammalian meat (veal, steak, ham, venison, bison, etc.). Other non-mammalian animals (fish, birds, frogs, snake, alligator, etc.) tend to have lighter-colored skeletal muscle meat due to the lack of myoglobin, amongst other factors.

That would be a working theory.