`pushers` table contains user device names, which may include user real names

This issue has been migrated from [#5830](https://github.com/matrix-org/synapse/issues/5830).

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The `device_display_name` column in `pushers` may be considered to contain personally-identifiable information.

Specifically, on my homeserver (which consists mostly of my real-life friends), I observe:

* RiotX/Andoid `device_display_name` corresponds to a `devices.device_id` – probably not PII or an issue
* Riot/Android `device_display_name` typically corresponds to a model of Android device — e.g. 'Moto G (5)'
* Riot/iOS `device_display_name` typically corresponds to ''s iPhone'
* Usually just first name, but in one instance, also their last name.
* It does not always correspond to this – it seems to be user-configurable as one of them is a bit of a funny string that has almost definitely been typed in by my friend somewhere
* I am not an iOS user so cannot really comment.

Do note that this is not the same as the `devices` table – I'm not sure if these `device_display_name` are displayed anywhere to users in actual Riot clients.
It can, however, be pulled out with the [GET /_matrix/client/r0/pushers](https://matrix.org/docs/spec/client_server/r0.5.0#get-matrix-client-r0-pushers).

With that in mind, it seems like it might be an issue belonging to clients rather than Synapse, but it's perhaps worth thinking about. In general, I would personally prefer to keep personal information (that hasn't been end-to-end encrypted) out of my database. It is my suspicion that users aren't aware that this information is being transmitted, and are not being given the choice to remove it.