"Still, I wonder why the name "Intercaribe" when we have so many chips with Intercontinental on them:"

What if the "Intercaribe" name was made up to represent all the Caribbean casino operations Bud was involved with?

What if Bud used them in his 1961 Belvedere restaurant? What if he called a back room the "Intercaribe?"

Lots of "What If's" with this chip.

That would not be my guess but "What if?"