Hi @Enzo Nguyen ,
Thank you for reaching out to Microsoft Q&A Forum.
Based on your description, I understand that you are trying to rename a document in the library, but the new name is not being reflected in SharePoint Search.
However, from my perspective, I am thinking that this article is contain the instruction that closest to your context:
Link article: Manually request crawling and reindexing of a site, a library or a list - SharePoint in Microsoft 365 | Microsoft Learn
Please go to your SharePoint site's document library > Click on Settings (at the top right) > Library settings > More library settings > Advanced settings > Re-index Document Library > then wait for 24 hours to see.
Note: Reindexing a site can cause a massive load on the search system. Don't reindex your site unless you've made changes that require all items to be reindexed.
If the issue persists after trying all the steps above, we recommend raising a support ticket via the Microsoft 365 admin center. Because, as a Microsoft Q&A agent, I don't have the necessary permissions to perform certain tests or access specific information that might be required to resolve your issue. Given the complexity of your case, it might require additional information and a more thorough review to resolve the issue effectively. The support team can further investigate and escalate the case to a specialized team if needed.
Reference: Get support - Microsoft 365 admin | Microsoft Learn
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