Change Azure virtual machine name in Azure portal

Credit to Oliver Miossec for this non-destructive azure powershell script that creates a new VM, with some changes for parameters. You can find his post here. It's extra awesome because it'll also fix badly-named discs and NICs associated with the machine.

#Deletes and recreates a VM
param (
    [Parameter(Mandatory=$true)]
    [string]$vmOldName,
    [Parameter(Mandatory=$true)]
    [string]$vmNewName,
    [Parameter(Mandatory=$true)]
    [string]$rgName,
    [string]$newLocation #Optional, moves the VM to a new Geographic Location
)

$ErrorActionPreference = "Stop"

Write-Host "Get and Shutdown old VM, Create new config"
$SourceVmObject = get-azvm -Name $vmOldName -ResourceGroupName $rgName

if ([string]::IsNullOrEmpty($newLocation)) {    
    $newLocation = $SourceVmObject.Location
    Write-Host "No new location specified, using the current VM's existing location: $newLocation"
}

$SourceVmPowerStatus = (get-azvm -Name $SourceVmObject.Name -ResourceGroupName $SourceVmObject.ResourceGroupName -Status).Statuses | where-object code -like "PowerState*"

if ($SourceVmPowerStatus -ne "VM deallocated") {
    stop-azVm -Name $SourceVmObject.Name -ResourceGroupName $SourceVmObject.ResourceGroupName -Force
    Start-Sleep -Seconds 30 #Wait to ensure VM is shutdown.
}

$NewVmObject = New-AzVMConfig -VMName $vmNewName -VMSize $SourceVmObject.HardwareProfile.VmSize 

Write-Host "Create new Network Objects"
$subnetID = (Get-AzNetworkInterface -ResourceId $SourceVmObject.NetworkProfile.NetworkInterfaces[0].id).IpConfigurations.Subnet.id

$nic = New-AzNetworkInterface -Name "$($vmNewName.ToLower())-0-nic" -ResourceGroupName $SourceVmObject.ResourceGroupName  -Location $SourceVmObject.Location -SubnetId $SubnetId 

Add-AzVMNetworkInterface -VM $NewVmObject -Id $nic.Id

Write-Host "Move OS Disk"
$SourceOsDiskSku = (get-azdisk -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName $SourceVmObject.StorageProfile.OsDisk.name).Sku.Name

$SourceOsDiskSnapConfig =  New-AzSnapshotConfig  -SourceUri $SourceVmObject.StorageProfile.OsDisk.ManagedDisk.Id -Location $SourceVmObject.Location -CreateOption copy

$SourceOsDiskSnap = New-AzSnapshot -Snapshot $SourceOsDiskSnapConfig  -SnapshotName "$($SourceVmObject.Name)-os-snap"  -ResourceGroupName $SourceVmObject.ResourceGroupName

$TargetOsDiskConfig = New-AzDiskConfig -AccountType $SourceOsDiskSku -Location $SourceVmObject.Location -CreateOption Copy -SourceResourceId $SourceOsDiskSnap.Id

$TargetOsDisk = New-AzDisk -Disk $TargetOsDiskConfig -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName "$($vmNewName.ToLower())-os-vhd"

Set-AzVMOSDisk -VM $NewVmObject -ManagedDiskId $TargetOsDisk.Id -CreateOption Attach -Windows

Write-Host "Create new Data Disks"
Foreach ($SourceDataDisk in $SourceVmObject.StorageProfile.DataDisks) { 

    $SourceDataDiskSku = (get-azdisk -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName $SourceDataDisk.name).Sku.Name

    $SourceDataDiskSnapConfig =  New-AzSnapshotConfig  -SourceUri $SourceDataDisk.ManagedDisk.Id -Location $SourceVmObject.Location -CreateOption copy

    $SourceDataDiskSnap = New-AzSnapshot -Snapshot $SourceDataDiskSnapConfig  -SnapshotName "$($SourceVmObject.Name)-$($SourceDataDisk.name)-snap"  -ResourceGroupName $SourceVmObject.ResourceGroupName

    $TargetDataDiskConfig = New-AzDiskConfig -AccountType $SourceDataDiskSku -Location $SourceVmObject.Location -CreateOption Copy -SourceResourceId $SourceDataDiskSnap.Id

    $TargetDataDisk = New-AzDisk -Disk $TargetDataDiskConfig -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName "$($vmNewName.ToLower())-$($SourceDataDisk.lun)-vhd"


    Add-AzVMDataDisk -VM $NewVmObject -Name "$($vmNewName.ToLower())-$($SourceDataDisk.lun)-vhd" -ManagedDiskId $TargetDataDisk.Id -Lun $SourceDataDisk.lun -CreateOption "Attach"
}

Write-Host "Creating..."
New-AzVM -VM $NewVmObject -ResourceGroupName $SourceVmObject.ResourceGroupName -Location $SourceVmObject.Location
Write-Host "VM Created..."

Ryanman already posted a script originally written by Oliver Miossec. However, this script only works for Windows VMs.

I added an argument (-osType) to specify the osType so it also works for Linux VMs.

Update 1: I updated the script to auto detect the Os of the Source VM

Update 2: Added new Parameter "-newSubnetId" which will move the VM to a new vnet or subnet (needs to be on the same subscription)

You need to specify the full URL of your subnetID like:

/subscriptions/<subscriptionID>/resourceGroups/<ressourceGroupName>/providers/Microsoft.Network/virtualNetworks/<virtualNetworkName>/subnets/<subnetName>

#Deletes and recreates a VM
param (
    [Parameter(Mandatory=$true)]
    [string]$vmOldName,
    [Parameter(Mandatory=$true)]
    [string]$vmNewName,
    [Parameter(Mandatory=$true)]
    [string]$rgName,
    [string]$newLocation, #Optional, moves the VM to a new Geographic Location
    [string]$newSubnetId #Optional, moves the VM to a new Subnet
)

$ErrorActionPreference = "Stop"

Write-Host "Get and shutdown old VM, Create new config"
$SourceVmObject = get-azvm -Name $vmOldName -ResourceGroupName $rgName

if ([string]::IsNullOrEmpty($newLocation)) {    
    $newLocation = $SourceVmObject.Location
    Write-Host "No new location specified, using the current VM's existing location: $newLocation"
}

$SourceVmPowerStatus = (get-azvm -Name $SourceVmObject.Name -ResourceGroupName $SourceVmObject.ResourceGroupName -Status).Statuses | where-object code -like "PowerState*"

if ($SourceVmPowerStatus -ne "VM deallocated") {
    stop-azVm -Name $SourceVmObject.Name -ResourceGroupName $SourceVmObject.ResourceGroupName -Force
    Start-Sleep -Seconds 30 #Wait to ensure VM is shutdown.
}

$NewVmObject = New-AzVMConfig -VMName $vmNewName -VMSize $SourceVmObject.HardwareProfile.VmSize 

Write-Host "Create new Network Objects"
if ([string]::IsNullOrEmpty($newSubnetId)) {    
    $subnetID = (Get-AzNetworkInterface -ResourceId $SourceVmObject.NetworkProfile.NetworkInterfaces[0].id).IpConfigurations.Subnet.id
    Write-Host "No new Subnet specified, using the current VM's existing subnet: $subnetID"
} else {
    $subnetID = $newSubnetId
    Write-Host "new Subnet specified, $subnetID"
}


$nic = New-AzNetworkInterface -Name "$($vmNewName.ToLower())-0-nic" -ResourceGroupName $SourceVmObject.ResourceGroupName  -Location $SourceVmObject.Location -SubnetId $SubnetId 

Add-AzVMNetworkInterface -VM $NewVmObject -Id $nic.Id

Write-Host "Move OS Disk"
$SourceOsDiskSku = (get-azdisk -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName $SourceVmObject.StorageProfile.OsDisk.name).Sku.Name

$SourceOsDiskSnapConfig =  New-AzSnapshotConfig  -SourceUri $SourceVmObject.StorageProfile.OsDisk.ManagedDisk.Id -Location $SourceVmObject.Location -CreateOption copy

$SourceOsDiskSnap = New-AzSnapshot -Snapshot $SourceOsDiskSnapConfig  -SnapshotName "$($SourceVmObject.Name)-os-snap"  -ResourceGroupName $SourceVmObject.ResourceGroupName

$TargetOsDiskConfig = New-AzDiskConfig -AccountType $SourceOsDiskSku -Location $SourceVmObject.Location -CreateOption Copy -SourceResourceId $SourceOsDiskSnap.Id

$TargetOsDisk = New-AzDisk -Disk $TargetOsDiskConfig -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName "$($vmNewName.ToLower())-os-vhd"

Set-AzVMOSDisk -VM $NewVmObject -ManagedDiskId $TargetOsDisk.Id -CreateOption Attach $SourceVmObject.StorageProfile.OSDisk.OsType

$NewVmObject.StorageProfile.OSDisk.OsType = $SourceVmObject.StorageProfile.OSDisk.OsType
$NewVmObject.StorageProfile.OSDisk.Name = "$($vmNewName.ToLower())-os-vhd"

Write-Host "Create new Data Disks"
Foreach ($SourceDataDisk in $SourceVmObject.StorageProfile.DataDisks) { 

    $SourceDataDiskSku = (get-azdisk -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName $SourceDataDisk.name).Sku.Name

    $SourceDataDiskSnapConfig =  New-AzSnapshotConfig  -SourceUri $SourceDataDisk.ManagedDisk.Id -Location $SourceVmObject.Location -CreateOption copy

    $SourceDataDiskSnap = New-AzSnapshot -Snapshot $SourceDataDiskSnapConfig  -SnapshotName "$($SourceVmObject.Name)-$($SourceDataDisk.name)-snap"  -ResourceGroupName $SourceVmObject.ResourceGroupName

    $TargetDataDiskConfig = New-AzDiskConfig -AccountType $SourceDataDiskSku -Location $SourceVmObject.Location -CreateOption Copy -SourceResourceId $SourceDataDiskSnap.Id

    $TargetDataDisk = New-AzDisk -Disk $TargetDataDiskConfig -ResourceGroupName $SourceVmObject.ResourceGroupName -DiskName "$($vmNewName.ToLower())-$($SourceDataDisk.lun)-vhd"


    Add-AzVMDataDisk -VM $NewVmObject -Name "$($vmNewName.ToLower())-$($SourceDataDisk.lun)-vhd" -ManagedDiskId $TargetDataDisk.Id -Lun $SourceDataDisk.lun -CreateOption "Attach"
}

Write-Host "Creating..."
New-AzVM -VM $NewVmObject -ResourceGroupName $SourceVmObject.ResourceGroupName -Location $SourceVmObject.Location
Write-Host "VM Created..."

Resource names for virtual machines are immutable. So, you will need to redeploy your virtual machine.

Best way to do this is to delete the current one, maintaining the disks, and then create a new one with the correct name pointing to those disks.