"Possibly one advantage of being a private company is being able to name drop?"

An NDA typically prohibits mention of the identity of a (potential) customer by the supplier to all third parties, not just publication of same by public news release.

A potential customer trying to stay ahead of its competitors would insist on an NDA with a private company, cuz even a private company would be happy to tell those competitors what potential customers have interest in the new tech. A big selling point which the customer wants to nip in the bud.