Pretty much any system with a real name policy both does and needs to let you change your handle, because preferred real (and legal) names change. Now, these systems often use email addresses as login names, but they sometimes also support changing the primary email address as well. In effect, identity is most likely managed by a surrogate key that isn't exposed.
Away from web services, gaming platforms like Nintendo's Switch allow for user name changes. As does the more enterprisey databases like ActiveDirectory (Windows logins), ldap and Linuxes / Unix passwd table also allows for login name changes.
To be honest, I've encountered more systems that do let you change your user name than systems that don't.