For consistent branding around all tools and technologies that could feasibly be used to build applications on top of Azure
That's still not good naming: Azure has so much services you could practically run anything on it. If keeping the Azure name to products actually running in the cloud it makes sense, otherwise it's just brand dilution.
That's not a super strong argument.. Visual Studio -> Azure Code Studio, TypeScript -> AzureScript, Windows -> Azuredows.. (Only a little tongue in cheek )
Originally it was built to manage SQL server instances on Azure.