This is the question the tool can't answer for you, and the one worth thinking hardest about.
Renaming a published URL breaks the old address. Every external link, bookmark, shared message and cached search result pointing at it returns a 404 unless you put a 301 redirect from the old URL to the new one. Google's documentation is unambiguous that a permanent redirect is what you use here.
Even done properly, expect a quiet period while the new URL is crawled and the old one's signals consolidate onto it. How long depends on how often the page gets crawled, which you don't control.
Two habits keep the damage small:
Redirect to the final destination, not the previous step. If /old-name already points at /newer-name and you rename again, point /old-name at the new address directly rather than letting it hop through. Chains accumulate quietly — across the sites we audited in the first half of 2026, redirect chains of two or more hops were among the ten most common failures our engine finds. Re-check yours with the redirect checker after any rename.
Update your own internal links. A redirect is a safety net for links you don't control. The ones inside your own site you can just fix, and leaving them pointing at a dead address wastes crawl budget for no reason. The internal link checker will show you which links on a page point where.
The practical conclusion: decide the slug before the page is published for the first time. After that, only rename when the URL is actively wrong — a typo, a product that changed its name, a path that contradicts the page. Tidiness is not a good enough reason.