comma use for list of adjectives describing an animal?

There is no need whatever for the commas.

Thank you for your reply. Would you mind expanding on that answer?

Use a listing comma wherever you could conceivably use the word "and" (or or) instead. Do not use a listing comma anywhere else.

A listing comma is used in a list of modifiers which all modify the same thing. Such a comma could be replaced by "and" without destroying the sense:

A large, red, ugly box
A large and red and ugly box

I observed one, adult, brown and black, male Yorkshire Terrier named “Buzz.”

All the commas except the first are OK. You would not use 'and' or 'or' after 'one'. You might conceivably write "one adult and brown and black and male Yorkshire Terrier named “Buzz.”

Most modern native writers would not enclose Buzz in quotation marks.