Chosen nickname/alias of a user should be respected (imported) when inviting them to a new space/room

**Suggestion**

This is a hopefully more useful evolution of the concept of pet-names for chats https://github.com/element-hq/element-meta/issues/725 (overriding real room/user names with custom display names https://github.com/matrix-org/matrix-spec/issues/188) by combining two in-progress ideas.

1. Support per-room display-names https://github.com/element-hq/element-meta/issues/499 (API for changing display name in a space/room https://github.com/matrix-org/matrix-spec/issues/103)
2. Canonical DMs / 1:1 chats https://github.com/matrix-org/matrix-spec-proposals/pull/2199 (element https://github.com/element-hq/element-meta/issues/1467 synapse https://github.com/element-hq/synapse/issues/6261)

If a user were to send a `/myroomnick ALIAS` command to a canonical DM, the other user in the room could automatically import that alias into any new spaces/channels when inviting the aliased-user. This would mean when inviting a user to any space/community, there would be a quick check against the canonical 1-on-1 chat for a preferred alias, then if one exists it would be copied into the room/space.

Note: It might be worth considering the privacy implications of this (maybe the user should accept the invitation and the alias separately?) similar to existing leaks of nicknames across homeservers https://github.com/matrix-org/synapse/issues/5677

Related:
* Decouple human-readable aliases from MXIDs: https://github.com/matrix-org/matrix-spec/issues/63 (per-space/room profiles https://github.com/matrix-org/matrix-spec-proposals/pull/3189 remove MXIDs from events https://github.com/matrix-org/matrix-spec-proposals/pull/1228)
* Decentralized accounts https://github.com/matrix-org/matrix-spec/issues/246 and identity https://github.com/matrix-org/matrix-spec/issues/203
* Rename users https://github.com/element-hq/synapse/issues/12174 forward MXID https://github.com/matrix-org/matrix-spec/issues/65 and transfer space/channel memberships https://github.com/matrix-org/matrix-spec/issues/238

Start by reviewing the linked proposals on per-room display names and canonical DMs, then examine the cited privacy concerns around nickname leakage. Done would require an agreed protocol design covering alias import, invitation timing, and user consent; the issue does not name implementation files or tests.

Written by the indexing model from the issue text.