If that clause is not in there, ask for a clarification.

Find out what a rider to cover named storms would cost you.

Also start contacting other insurance companies about their homeowners policies in your area.

It is fairly common for such policies to routinely exclude the things you are most likely to be a great risk for. Earthquake insurance if you live near the San Andreas fault is usually quite pricy. If you live anywhere close enough to the coasts where named storms do sometimes wind up, that's why. In any one specific spot it is usually years, sometimes many years, between the actual arrival of named storms. But you're at far greater risk than I am, living in northern New Mexico. It doesn't have to be a frequent occurrence, but enough of a risk that the company just doesn't want to be on the hook when such a storm comes through and now they have hundreds, maybe thousands, maybe even tens of thousands of policies they have to make good on.

Good luck. I hope you get this resolved soon.

Get it in writing....

and it's become a joke in my family. But now I wonder if there is something more to it. They have a lot of insurance companies who advertise there. Hmm.

I found out that I have certain 'named storm' coverage but if the storm is 'named' my deductible goes from $1000 to $5000. My policy does not cover earthquake or tornado damage. I am not in an area where these events occur but with all the changes in weather and seismic activity, who knows.
I also do not have federal flood insurance. That is an option I cannot afford and is a Federal program, not something I'd find on my policy.

As posted on the above reply, I also noticed that our regional weather reports seemed to name certain snowstorms last winter. I don't know if this is a national name-giving or something our local weather folks coined.

I will re-read my policy tomorrow to see if I can find where it is written about named storm coverage. If I can't find it, I will go to the agency and ask for a copy of that clause. The policy has so many clauses, whereas-es, what-ifs whatever, it makes long, boring, confusing reading.
Simple wording is beyond these businesses.