Sony is starting to offer beta invites for the upcoming PS4 firmware update that will allow username change. There is a major caveat though if you want to avail this offer.
The username change invites are going out for most people in Europe. If you haven’t received one so far, chances are that you are not a part of the early batch. In that case, have some patience and wait until you are selected. Here is what is being sent in the email regarding the PS4 firmware update 6.10 beta. (source)
Change Online ID Overview
As part of the System Software 6.10 preview, we are rolling out the upcoming Change Online ID system feature. As a preview user you will be able to change your Online ID using the new system tools.
To use this feature please ensure you have a clear understanding of the implications of changing your Online ID and the software’s restrictions – described in the following sections – before software installation. If you are unsure, do not download and install the Preview Programme software.
There is a big risk involved as you can read here if you decide to change your username, so make sure to read the issues carefully before making the plunge, unless you hate your username enough to ignore this matter.
PS4 Firmware Update 6.10 still doesn’t have a detailed changelog or official release date, but judging from the release of the last couple of system software updates, this can take 1 month or more to release while the username change will remain in beta phase until next year.