カフェインゼロって英語でなんて言うの？

When you are talking about a soft/fizzy drink you would use the term 'caffeine free' but if you were ordering a coffee you would use the term 'decaffinated' or decaf for short meaning it has no caffeiene in it

Whatever you order at Starbucks, just ask them to please make it "decaf", as in "I would like a tall, decaf vanilla latte, please."
This is short for "decaffeinated", or "without caffeine".

Another way of saying this could be "caffeine free", meaning free from caffeine. This is a less common phrase than decaf.

(In fact, I just went to Starbucks myself and ordered a decaf coffee!)

Caffeine-free is usually the term you will see on soft drinks, coffee, or tea that does not have caffeine. You can also say something is non or not caffeinated. Adding either of these to the beginning of a word make it the opposite, but caffeine-free is the most common way of stating something has zero caffeine in it.

The term you're looking for is "decaf".
There are some other names to it, but this one will suffice as it's
the most used one.
Here's how to use it in sentences:
A: Hi, what can I get for you?
B: I'd like a decaf coffee, please.

The two nouns you see provided above are what we use to refer to coffee that does not have any caffeine in it. With other drinks, like soda or tea, it may simply say caffeine free. Sometimes diet sodas or sodas that have the label zero also have no caffeine, so it would be a good idea to check the ingredients.