Username changes are always public by default.
How long a username change is public for and visible to everyone is controlled by the option usernameChangeRecentLimit
. By default, the username change is publicly visible for 30 days.
If you prefer username changes not to be visible publicly to others at all then you can change this limit to 0.
A user will always be able to see their own username changes and staff with the relevant permission (Bypass user privacy) will always be able to see a user's full username change history regardless of this option.