Device name privacy: is MAC randomization enough?

The point of randomizing MAC address is to make it harder for local Wifi providers to track you.

But I noticed that device name is also broadcasted when turning on Bluetooth an even when connecting to a Wifi router. So there is still a possibility to be tracked if device name is unique.

I thought about choosing a generic name like "John's iPhone" to "blend in". But still, I'd like to know if there's a better way.

address bluetooth device iphone john local mac mac address name point privacy randomization router thought wifi