before their color? How do you get a custom pet?

It means someone paid 500csc or cash shop credits to be able to upload an overlay for their pet that shows up all around the site. If you hover over personal then click pets the next page will have a few options, one of which is "Custom Overlays". That's where you go to pay for it.

You can get the same effect by using css on pet profiles without paying. However it doesn't show up all over the site, just on their profile.