Different parts of puberty have different names:
Pubarche is the name for attaining pubic hair.
Thelarche is the name for breast growth.
Adrenarche is the name for a time of increased hormone production.
Menarche is the name for first period.
Spermarche is the name for first ejaculation.
Gonadarche is the name for when the testicles and ovaries enlarge.