Back in the War Rig, Furiosa is dying. Her lungs are collapsing, but Max knows what to do.
After a quick, "I am so sorry," he jams a knife into her lung.
Furiosa can breathe better, but she's lost a lot of blood.
Good thing Max is a universal donor then, right? He transfuses his blood into Furiosa.
As she lies there, in and out of consciousness while his blood flows through her veins, he cradles her head and says, "Max. My name is Max. That's my name."