Not allowing your name to be used is quite normal. Company I know doesn't allow other companies to show that they have that company as a customer.
Reason for that is branding. The other company is basically advertising using the name of another company. That is a big no. It is sort of saying "company X buys from us, so you should too".
We found out a vendor was using our name to pimp their products to other distributors. That vendor was then caught with bad policies that allowed their product to become infected with malware. As we were dealing with that issue, we got a call from one of our competitors asking if we were infected as well, as they knew we used the same product from the same vendor.
You're absolutely right, keeping your brand carefully under your control is absolutely critical.
Reason for that is branding. The other company is basically advertising using the name of another company. That is a big no. It is sort of saying "company X buys from us, so you should too".