It needs to be doable through the device’s settings. Eg. An android phone has the option to rename how it appears to other devices, while a speaker can’t do that

After you change the name of the device.

Unpair the device and re-pair it.

You can’t. The BT name is baked into the device’s firmware and will always show up as that on newly paired devices.

The best you can do is rename it on devices that allow it like Android or iOS.