cask: improve consistency of rename handling #24016

• Keep rename behaviour consistent with its intended use.


• Cover additional input cases and clarify the cookbook guidance so future changes preserve the same expectations.

• [x] Have you followed our Contributing guidelines?


• [x] Have you checked for other open Pull Requests for the same change?


• [x] Have you explained what your changes do? Performance claims (e.g. "this is faster") must include brew benchmark results.


• [x] Have you explained why you'd like these changes included, not just what they do?


• [x] For bug fixes, have you given step-by-step brew commands to reproduce the bug?


• [x] Have you written new tests (excluding integration tests)? Here's an example.


• [x] Have you successfully run brew lgtm (style, typechecking and tests) locally?

• [x] I did not use AI/LLM to create this PR, or I disclosed the tool/model below and reviewed its output; I did not attribute commits to AI and will answer maintainer questions and review comments myself without AI/LLM.

Codex with GPT 6 Astra at Extra High effort, with local review and testing.