What is the name of the process where Rubisco fixes oxygen instead of carbon dioxide?

Photorespiration is the process that begins when Rubisco fixes oxygen instead of carbon dioxide.

Rubisco normally catalyzes the attachment of carbon dioxide to RuBP in the Calvin cycle. However, its active site can also react with molecular oxygen. That oxygenation reaction produces one molecule of 3-phosphoglycerate and one molecule of 2-phosphoglycolate, a compound that cannot continue directly through the Calvin cycle.

Plants recover much of the trapped carbon through a salvage pathway that moves metabolites among chloroplasts, peroxisomes, and mitochondria. The pathway consumes energy and releases some previously fixed carbon as carbon dioxide, so photorespiration reduces the efficiency of photosynthesis.

The name can be misleading: photorespiration is not ordinary cellular respiration, and it does not generate useful ATP in the way mitochondrial respiration does. It becomes more significant when temperatures rise, stomata close during drought, or carbon dioxide inside the leaf falls relative to oxygen. C4 and CAM plants have carbon-concentrating strategies that greatly reduce it.