When you update the SharePoint Online site title. It should reflect everywhere like in search or if you go to admin center and search under active site.
If you want to update site title , click on setting icon and select site information. Now you can update the site name and site description and click on save button. It will show you updated title on the site.
You might encounter with an issue where updated site name/title does not reflect on the SharePoint search and admin center
If you try to edit the site title on the admin center and save the updated name, after few second it gives you the old name. You have already tried to reindexed the site but result is not expected
Due to sync issue this issue occurs, you can update the site title through PowerShell command and it will fix the issue.
Connect-PnpOnline -Url “yourSiteUrl” -interactive
Set-PnPWeb -Title “newTitle”