The character 寵(宠) is a picture of a dragon under a roof, and originally meant to revere or honour (尊崇 zūn chóng) because if you have a dragon in your house you better be really polite.*
Later the meaning broadened and mellowed, you’ve probably seen it as:
寵愛(宠爱) chóng ài to dote on someone
As a grandma dotes on her grandchildren. But this can go too far and then you get
寵壞(宠坏) chóng huài to spoil a child
And from these meaning it did not take long to evolve into
寵物(宠) chóng wù (house) pet
Like a dog, cat or (small) dragon.
* The character 寵(宠) goes back three thousand years to the Western Zhou dynasty, and has not changed in all that time: Actually it’s just a simple radical / phonetic construction, the roof radical 宀 (mián, usually known as 宝盖头) is used with characters meaning respect (官 guān official, 宦 huàn officialdom) while 龙 lóng is just there for the sound.