What is the process of gamete formation known as?

The gametes sperm and egg are formed in the gonads testes (in males) and ovaries (in females) respectively. 

The germ cells in the testes and ovaries undergo meiosis and divide twice to form four daughter cells. This process in which the gonads produce gamete cells is called gametogenesis. 

Gametogenesis in males produces four sperm cells and is known as spermatogenesis while in females it produces one egg cell and three polar bodies and is known as oogenesis.

Each gamete cell is haploid and carries half the number of parental chromosomes.