Think about it this way
In real life in order to change your "Name" you'd have to go to a government agency and pay a sum of $$ to have it changed
In runeterra i'd imagine its the same
You're a summoner come to the league in order to support your faction ( Noxus, Demacia, ETC )
I'd imagine before you became a summoner you lived somewhere on this world within one of the many major cities ( Perhaps you're a yordle? Perhaps you're a freljordian ) anyhow I think you get my point
its a lot of paperwork to change someones set name so the IP you pay is an incentive for the Summoners Institute of War to allow this name change ( Wouldn't imagine anywhere else you could go to change it as MOST and I empthasize the "MOST" of Runeterra seems to be in the medieval ages ) Perhaps the summoners institute of war gave you your summoner name as a way to address you ( a nickname of sorts ) and your user is your true name..
But w/e I'm getting off track
Basicly its that expensive so people don't spam it and cause problems with the server ( could you imagine if 1000's of people swapped every 5 sec's ? )