docs: Document instance rename in HQ

CLAUDE.md

@@ -551,6 +551,20 @@ The control plane refuses to change an `hq`-sourced user's role or delete it
 the portal, but the API is the boundary; the UI is a courtesy. There is no local
 password-change endpoint at all, so there is no competing writer for the hash.
 
+**A rename moves the host, and the licence does not care.** `PUT
+/api/instances/:id/name` re-derives the slug from the new name through
+`provision.RenameSlug` — the same rules that named the instance at creation —
+and writes the control plane first, because `instances.slug`'s unique index is
+what settles a race between two accounts reaching for one name. A taken slug is
+a refusal, not an `acme-2`: creation appends a counter because any free slug
+will do, and a rename is a request for one specific host. A licence binds the
+instance UUID, so nothing is reissued and Paddle is not called. The old host
+keeps resolving for up to 60s (`instancehost.go`'s cache, which admin cannot
+reach into), and `km_session` is host-only, so the customer signs in again on
+the new address — the portal says so rather than redirecting them into a login
+screen with no explanation. The 24h cooldown lives on `admin_instances.renamed_at`
+because it is admin's policy; staff bypass it and must not write the field.
+
 ---
 
 ## Auth and Orgs
@@ -692,6 +706,7 @@ GET  /account                                  # account, instances, max_relinks
 POST /instances                                # create a cloud instance (Free tier, one Free per account per deployment)
 POST /instances/:id/renew                      # Free renewal; refuses outside the renewal window
 POST /instances/:id/claim-free                 # issue Free on a linked self-hosted instance
+PUT  /instances/:id/name                       # rename a cloud instance; moves its slug (owner|admin, 24h cooldown)
 POST /instances/link · /instances/:id/relink
 GET  /instances/:id/entitlement
 GET  /checkout/options                         # active plans + catalogue prices for the running PADDLE_ENV
@@ -717,6 +732,7 @@ Staff-session (`/api/staff`):
 GET,POST /accounts · GET /accounts/:id         # search by name, email, Paddle ID or instance UUID
 GET,POST /instances · GET /instances/:id       # instance + account + licence history + injection state
 POST /instances/:id/issue · /instances/:id/relink
+PUT  /instances/:id/name                       # rename any instance, no cooldown
 GET  /licenses · /subscriptions · /audit · /plans · PUT /plans/:deployment/:tier
 GET,PUT /catalogue
 GET,PUT /instances/:id/entitlement