Rename user

This issue has been migrated from [#12174](https://github.com/matrix-org/synapse/issues/12174).

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One of my users would like to change their Matrix ID (staying on the same server). I would like to support them.

I know about https://modular.im/tools/matrix-migration, but as the SSO (SAML)-Account stays the same, the two accounts won't be usable at the same time. Also I would prefer to make the process as painless as possible for the user.

An ideal solution would be an admin API call which:
1. creates the new account
2. points the `external_id` to the new account
3. adds the new account to the same rooms (with the same permissions) than the old one
4. associates the key backup with the new account

At the next login the user would be asked for the recovery key and have access to all rooms and messages like before.

An alternative solution could be to have the new account work like an alias for the first one. This would would mark the two accounts as "belonging to the same person" and thus other servers could treat them like they would be the same account.

There are discussions about [server independent accounts](https://github.com/matrix-org/matrix-spec/issues/246) and [moving accounts between servers](https://github.com/matrix-org/matrix-spec/issues/238) but this request seems smaller to me.

keywords: migrate account, change mxid, localpart