What is the name of the Vulcan mating drive?

The Vulcan mating drive is called pon farr.

Pon farr is a recurring biological condition in Vulcan life, generally described as occurring every seven years in adult Vulcans. During it, powerful physiological and emotional pressures overwhelm the strict emotional control for which Vulcans are known. The condition was introduced in the Original Series episode “Amok Time,” when Spock must return to Vulcan.

The episode links pon farr to Vulcan marriage customs and the ritual challenge known as koon-ut-kal-if-fee, often translated as “marriage or challenge.” A challenger may fight the bonded male, traditionally in a battle to the death. The ceremony helps explain why Spock’s private crisis becomes both a medical emergency and a family conflict.

Pon farr is often misunderstood as meaning Vulcans can mate only once every seven years. That is not established as a general rule. Writer and story editor D. C. Fontana clarified that Vulcans can have sexual relationships outside pon farr; the seven-year cycle is the period of overwhelming biological compulsion, not the entirety of Vulcan sexuality.