In the US, they are assigned by a division in the FAA called Aeronautical Information Management (AIM), per FAA Order JO 7400.2J (Procedures for Handling Airspace Matter), section 3-3-2:
a. Service area office are responsible for assigning and changing names of NAVAID and aeronautical facilities, and must follow the instructions contained herein and in FAAO JO 7350.8, Location Identifiers, Chapter 1.
b. AIM is responsible for issuing five−letter names for radio fixes, waypoints, marker beacons, and compass locators. Five−letter names must be issued by AIM to the Terminal Procedures and Charting Group, Major Military Commands (MAJCOM) and Air Route Traffic Control Centers (ARTCC) for future assignments.
It's conceivable they accept suggestions from ARTCCs or other entities. I don't know. I doubt paid sponsorship is approved but have no first hand knowledge there. Suggestions are probably casual and intormal.
They are often quite amusing, like ITAWT ITAWA PUDYE TTATT. Very often enroute fixes are named for small towns or other points of interest near the fix.