Connect-AzAccount does not correctly set the name of the environment

[faix]

Description

I have some additional environments like for example:

$azEnv = (Get-AzEnvironment -Name AzureCloud)
$azEnv.Name = "$"
$azEnv.ResourceManagerUrl = "https://centraluseuap.management.azure.com/"
$azEnv | Add-AzEnvironment

If i start with no context and do Connect-AzAccount -Environment CentralUsEuap

Its all good. But then i do Connect-AzAccount -Environment AzureCloud

And the resource manager url has changed, yet the name of the environment has remained the same...

The inverse is also true, i can start with AzureCloud and then swap, and the Name will stay as AzureCloud instead of swapping to CentralUSEuap

Issue script & Debug output

N/A

Environment data

Name                           Value
----                           -----
PSVersion                      5.1.20348.4294
PSEdition                      Desktop
PSCompatibleVersions           {1.0, 2.0, 3.0, 4.0...}
BuildVersion                   10.0.20348.4294
CLRVersion                     4.0.30319.42000
WSManStackVersion              3.0
PSRemotingProtocolVersion      2.3
SerializationVersion           1.1.0.1

Module versions

ModuleType Version    Name                                ExportedCommands
---------- -------    ----                                ----------------
Script     5.3.0      Az.Accounts                         {Add-AzEnvironment, Clear-AzConfig, Clear-AzContext, Clear...
Script     6.4.0      Az.KeyVault                         {Add-AzKeyVaultCertificate, Add-AzKeyVaultCertificateConta...
Script     7.22.0     Az.Network                          {Add-AzApplicationGatewayAuthenticationCertificate, Add-Az...
Script     8.1.1      Az.Resources                        {Export-AzResourceGroup, Export-AzTemplateSpec, Get-AzDeny...

Error output