Traditional pet's name in Japan and other countries?

Right! Could someone write how do you name a pet in japanese?
example:
In one anime, I fount that traditional name for a bird is
'Bi-Chan'. Don't know if that's true, so I would like to know (^_^)

In poland it would be:
for a dog:
Misiek (Mishieku?), Rex, As, Burek, Azor

for a cat:
Mruczek
(if you want to call the cat, you say to it
[read in japanese] 'Kichi-Kichi-Kichi';
in english 'Kiri-Kiri-Kiri')

for a guinea pig:
Kubuś (Don't know if polish special 'S' is visiable.)
Kubus (read in jap. Kubushi)

Don't know if thouse are the all name, if someone knows some more names, then I'll write them down.

So how do you call your pets in other countries?

most common dog name in japan is "Pochi"
most common cat name in japan is "Tama"
(Recently, not so common anyway. )
or they named from their color. like "kuro" "shiro"
birds and pigs? there's no common name in japan.

just for reference, my mom's dog name is "noir"
She is black Labrador Retriever. "kuro" is a much manly. so we named her "noir".

in my country oman, we use names that r easy for example: mimi . boby, lulu, lala and so on..