We're aware of the issues that are affecting the display name system in that while some players have been able to claim new names, unfortunately others have encountered problems and delays.
The issues are due to the amount of traffic being directed towards the part of the website and game module that deals with display names. We have launched some fixes to ease the current issues and will continue to look for improvements, but we can only ask for your patience at this time.
We've noticed that some players who are trying to use the website are refreshing too often and are hitting the 'anti-bot' protection limits, and therefore seeing a "page not found" message, so try reducing the frequently of requests & page refreshes to avoid this. Alternately we recommend you use the in-game Change Name function which can be found in the Hero interface.
The team will be investigating other ways in which we release future batches to help prevent similar issues from occurring.
Once again we apologise for any inconvenience caused.
The RuneScape Team