Can I change the SharePoint user password?
By central administration or by code?
I'm using SharePoint 2013 on Windows Server 2008 R2 standard.
if you are talking about the SharePoint Services accounts which use to run services / App Pools etc, I am guessing those IDs are already in the SharePoint Managed account sections.(to understand read this).
if you want to change the Managed account password, you have both choices either central admin or Powershell.
You have couple of options in the SharePoint, from central > Security > Configure Managed Account....
you can change the password directly from SharePoint to AD with random password. From Powershell you can take the advantage of Set-SPMangedAccount
$m = Get-SPManagedAccount –Identity "DOMAINx\UserY" Set-SPManagedAccount -Identity $m –AutoGeneratePassword true