What organisation owns intersection names? I understand that five letter intersection codes (such as WARPI, PAPPI, KUBBS, ROSLY, ZALPO, ...) are unique in the world.

However, their names don't comprise a national prefix (as aircraft tail number do, or airport codes do), which would allow to delegate name bookkeeping to the individual countries's aviation authorities by prefix. 

Therefore, a single, international organization has to somehow own and disambiguate all the intersection names. I would expect the ICAO to be that organization, but I haven't been able to find any resource mentioning that.

Help?
The allocation of waypoint names is actually handled by each country's individual aviation authority. This means that there are actually duplicates in different countries or regions. The ICAO has made at least two attempts to remove the duplicates and make the names globally unique, one in 2010 and another in 2018. Despite these efforts, there are still over 1000 duplicate waypoints in the ICARD database.