What do Japanese say when they call their pet cats/dogs?

Question

We sometimes say in English,

Hey kitty come over here.

Do they say,

CatChan iku yo...

Answer 1

We call our pets by their (nick)names most of the time.

[ The pet's name (+ chan to show extra affection)］、 こっちおいで。([...], kocchi oide.)

You can replace the name with generic terms like 猫ちゃん(neko-chan; kitty) and ワンちゃん(wan-chan; doggy) if you don't know what they are called.

行くよ(iku yo) means "let's go", by the way.