Brand

oYo
Royal
Beta
Testing
AZ
JE
BetaGift
Pride
4th July - Released on breedings over only a 2 day period, this can pass.
Atlantis
HealingBlue - Inherited from Kallen/Indigo or Lavender
HealingPink - Inherited from Zinnia or Rosemary
SpiralEarth
SpiralFire
SpiralWater
SpiralLight
SpiralAir

HopeHeart
HopeGreen
HopeRed
Skull (from Hallween 2017)
Blood (from Hallween 2017)
Stars
Snowflake
Cupid
ForeverLove
Bunny

Zodiac signs

The Zodiac brands come with 1:100 chance in that month, if parents don't pass the brand

Leo (August 2017)
Virgo (September 2017)
Libra (October 2017)
Scorpio (November 2017)
Sagittarius
Capricorn
Aquarius
Pisces
Aries (April 2018)