Bluetooth naming iPhone 11

There are two aspects to it, as I understand

1. There are devices which offer renaming. To understanding it better; there is a set of information transmitted by a bluetooth device to identify itself: generally known as "SDP packet" which includes a universally unique identifier (UUID) and a list of other available services. What Mac does is, it keeps a link of the new name provided by the user to that of UUID (Usually the last part) received from the device. iOS device is capable of renaming such devices which offer services to rename / rewrite the last part of the UUID on the device itself.
2. On a Mac we may simply assign a Nick name for a bluetooth accessory and not changed its name. Had we renamed a bluetooth accessory using a Mac and paired it with another device then the new name must appear on all other devices. Presumably, I am sure that is not the case with the kind of action that we have taken to nickname.

Hope I was able to put my thought across through what I have leant through my experience.

Depends on the source. Some support renaming, most do not.

If the specific Bluetooth device supports renaming it will be in the (i) menu for it in Bluetooth settings.

See here: Change the name of a Bluetooth accessory - Apple Support