A tool's wire-visible name (`customWireName`) is rendered into the
system prompt body via `toolPromptNames`, but the applied-tool signature
only hashed name+label+description. A future tool whose wire name varied
without touching the other fields would silently produce a stale system
prompt that advertises the wrong callable name to the model — desyncing
prompt guidance from actual tool routing.
Today the only mutation path (edit-mode toggle) is also covered by a
description change and an explicit `refreshBaseSystemPrompt` from
`#syncEditToolModeAfterModelChange`, so this is a defensive fix rather
than a live bug. Including `customWireName` makes the signature a
self-consistent model of the prompt inputs.
- Extended `describeTool` in `#computeAppliedToolSignature` to include
`tool.customWireName ?? ""`. Applies to both the active-tool segment
and the (mcpDiscoveryEnabled) registry segment via the shared helper.
- Updated the docstring to call out wire-name coverage.
- Added a regression test that mutates `customWireName` between
identical-metadata refreshes and asserts the rebuild fires.
Per Codex review on #890.