Fix "Connect-SPOService : The term 'Connect-SPOService' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again." Error

Problem: When trying to connect to SharePoint Online through PowerShell cmdlet: Connect-SPOService -URL https://crescent-Admin.SharePoint.com, Got an error message:
Connect-SPOService : The term 'Connect-SPOService' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again.

Solution:
This error message indicates that the particular cmdlet doesn't exist in the loaded modules. Here in this case, this error is because: The "Connect-SPOService" cmdlet is part of SharePoint Online Management Shell (or SharePoint Online PowerShell Module) and its not loaded! So you must install SharePoint Online Management shell first, before using this cmdlet. You can download and install SharePoint Online Management Shell to your client machine from https://www.microsoft.com/en-us/download/details.aspx?id=35588

If its already installed, try uninstalling and then re-installing.

Double check if the SharePoint Online PowerShell Module is installed by:

Get-Module -Name Microsoft.Online.SharePoint.PowerShell -ListAvailable | Select Name,Version 

You can install the SharePoint Online PowerShell Module with:

Install-Module Microsoft.Online.SharePoint.PowerShell 

For un-installation, try:

Uninstall-Module -Name Microsoft.Online.SharePoint.PowerShell -AllVersions -Force

Although we don't have to explicitly load the module in PowerShell with "Import-Module Microsoft.Online.SharePoint.Powershell", give it a try to expose any potential issues.

If you are trying to connect to SharePoint Online PowerShell through a proxy server, the Connect-SPOService cmdlet connections fails! You have to use:

#Get Credentials to connect
$cred = Get-Credential
[System.Net.WebRequest]::DefaultWebProxy.Credentials = $cred

Connect-SPOService -Url "https://<Tenant-admin>.sharepoint.com" -Credential $cred