I think this depends on the semantic basis one uses for “hole”.

1 hole: One might say there is a single hole in a straw. The logic there is that the straw is a cylinder, so the inner surface at the top is a part of the same surface at the bottom. In that sense, a hole itself is a kind of cylinder with a single connected surface. But this could be taken as problematic, since the same argument means that the straw itself is a hole, or at least that it is made up entirely of the exact same things a hole must have, and nothing else.

2 holes: Where that fails is if one instead assumes the more abstract sense of “hole”. Consider the straw as a vessel with a volume – with both ends plugged, it holds a substance. One can unplug either end and argue that it is a hole since the substance within is now open to the outside by way of that hole. In that sense, there are two abstract holes in a straw (abstract because the connection between both holes is ignored – neither hole is taken to have any depth – and each hole is an absence of material). Of course, due to physics, unplugging one end of the straw does not release the substance within if the other end is still plugged, but that holds no consequences for the logic of hole-as-absence-of-material.

0 holes: The argument could go further. One could try and solve this by considering other objects and how we think about “hole” in those contexts.

How many holes are in a bucket? If it’s a perfectly undamaged bucket, people would likely be arguing between two different values: in one sense, the bucket has a single hole, because there is an opening at the top. However, using the same logic that straws have a single hole, the bucket in fact is made of its hole, and it seems silly to say the bucket itself is a hole.

If one goes with hole-as-absence-of-material, then there’s a single hole in an undamaged bucket, but the bucket isn’t made up of hole.

Further still, one might argue instead that an undamaged bucket has no holes. Why? Because a liquid in such a bucket will not leak out of anywhere. The bucket is effectively a round piece of material formed into a shape, and that material itself contains no holes in an undamaged bucket.

Using that logic with the straw, an undamaged straw might actually be claimed to have no holes – but how? We’ve all likely used a straw that was bent or damaged and is less useful as a straw because pressure escapes from somewhere between the ends. Such a straw could be said to have a hole in it. There, “hole” has some aspect of brokenness being taken as part of its meaning. If the pressure-vessel part of the straw functions correctly, then it has no holes.

In popular culture: Consider the following lyric from Funkadelic: “What is a pipe but a pole with a hole in it? A pole is a pipe with no hole in it.”

There, the band has clearly relied on the 1-hole analysis of a pipe (taken to be relevant to the straw discussion since it seems uncontroversial to claim that a straw is a small pipe). Had they said “no holes in it”, the suggestion would have been that the band agrees with the abstract hole-as-absence-of-material sense. Similarly, it does not appear that the band thinks there are no holes in a pipe; in fact, that would be directly contradictory to their statement. But no logic is given directly for that choice in the song; one must extrapolate their position by context.

tl;dr A straw could be taken to have 0, 1, or 2 holes in it depending on the semantic sense of “hole” one selects. I need to think about this more like I need a hole in the head, but I also don’t know how many of those I have.