Rumor: an update of PS4 will introduce the ability to change your PSN ID
So far, Sony's answer to these requests was that such a feature was impossible because of how it was designed its network because the PSN ID is tied to purchases and to all our other activity on the PlayStation Network and games.
As discovered by a user on NeoGAF forums , it seems that Sony has been able to overcome obstacles and that this feature might soon be available to users. The user has analyzed the version 4.14 release notes of the Unreal Engine, finding several references to a passage by the use of "Online ID" (note the PSN ID) to an "Account ID", apparently a user's identifier is not linked to your username. These changes were made at the request of Sony, which seems so is preparing to release the PSN ID system in games to allow users to change it freely in the future.
For now there are no official announcements by Sony and it might take even long before this happen, because probably all games will have to be updated to stop using the PSN user ID, but we hope that sooner or later this thing come true. Obviously we will update you as soon as there will be news on this: stay tuned!