There were various schemes aimed at raising money for aircraft. The Ministry of Aircraft Production encouraged individuals, groups and companies to run "Spitfire Funds" and for a nominal £5000 donors could choose a name for their aircraft.
National Savings organised "Wings for Victory" campaigns, usually in towns and cities. As far as I'm aware there was no specified target figure, and some cities could raise enough for several bombers. I don't think they had the option of naming aircraft, and obviously names could be applied by the crews who flew them.
As mentioned earlier, the Air-Britain book "Gifts of War" has a lot of information on such schemes and the aircraft funded by them, including brief histories of every Spitfire named under the MAP scheme and a list of First World War presentation aircraft.
Lady MacRobert also paid for (IIRC) four Hurricanes, named after her sons.