What is the fear of confined spaces called?

Claustrophobia, and what triggers it is usually not the size of the space but the belief that you cannot get out - people who are fine in a small room become distressed in a larger one with a locked door. It is best understood as a fear of restriction and suffocation rather than of enclosure as such.

It is common enough to be a practical medical problem. A significant minority of patients cannot tolerate an MRI scanner - a tube you must lie still inside for up to an hour while it makes a very loud noise - and a share of scans are abandoned or need sedation. That is a large part of the commercial case for open and wide-bore scanners, which produce slightly worse images and get used anyway.

The evolutionary account is more plausible here than for most phobias. Being trapped, buried or unable to breathe has been a genuine and recurring cause of death for our ancestors in a way that spiders largely have not, and an aversion to it costs almost nothing. It is also one of the conditions that responds well to gradual exposure, and virtual reality treatments work - which is odd, given that the patient always knows they can take the headset off.