When you add a new disk to an existing VM, you can only modify the  disk name and size which means you are stuck using the current/default storage account (see https://azure.microsoft.com/en-us/documentation/articles/virtual-machines-windows-classic-attach-disk/)

Using PowerShell, you can specify a different storage location for your new data disk though (see https://msdn.microsoft.com/library/azure/jj152837.aspx)

o Make sure you use -MediaLocation parameter as per the documentation “[i]f no location is specified, the data disk will be stored in the VHDs container within the default storage account for the current subscription.”

o The disk label you enter in the command shows in the storage view, but under the VM dashboard the disk title will look like this: [CloudService]-[VMName]-[LUN #]-[Date/time stamp].  If you expand the VHD column (copying it into notepad may be easier) you will be able to see the full VHD name and that WILL match what you specified in the media location parameter.

Example: Get-AzureVM -ServiceName “NLW-MAGBox” -Name “NLW-MAGBox” | Add-AzureDataDisk -CreateNew -DiskSizeInGB 128 -DiskLabel “NLWTest” -LUN 0 -MediaLocation “https://storage2.blob.core.usgovcloudapi.net/mycontainer/MyNewDisk.vhd” | Update-AzureVM

*previously posted at https://blogs.msdn.microsoft.com/nicole_welch/2016/09/azure-classic-portal-how-to-add-a-data-disk-using-a-different-storage-account-than-the-os-disk/