The name change from 'Azure Active Directory' to 'Microsoft Entra ID' makes sense because AAD has nothing to do with Azure resources and little to do with Active Directory.
How many of you knew someone who believed that Azure AD meant an instance of Windows Server in Azure running a domain controller? Extend that concept to the entire set of Microsoft 365 services with 'Azure' in the name. It doesn't belong there. 'Azure Information Protection' is another example that comes to mind.
Modifying a name/title/label will present challenges, but it's often necessary. 'Microsoft Windows Azure' was likely changed to 'Microsoft Azure' because referencing the Windows OS was extraneous & misleading. Similarly, 'Office 365' was probably rebranded to 'Microsoft 365' because the scope of services is much, much wider than the desktop apps we're all familiar with.
Regarding updates to your company's internal documentation, I predict that a GitHub contributor will write a PowerShell script that backs up a specified directory's files and then generates a new directory whose contents (files of type docx/md/txt/etc.) have the appropriate replacements. Perhaps an AI will be necessary to distinguish between low-risk text (e.g., a mention of Azure AD in general) and high-risk text (like hostnames/DNS names) whose character string contains 'AAD' or 'AzureAD'.
So relax. This transition will be easier than you think. I'll end this post by encouraging all IT professionals to watch John Savill's upcoming response video on YouTube.