Theres a free username change that comes with osu!supporter, but that obviously costs money too. The only way to change username for 100% free is to have someone gift you osu supporter, the best way to do this is by winning a giveaway on somewhere like twitter ir the forums, or by winning a tournament or other osu competition. There is no other way unfortunately.
If your current username contains personal info or if you want to change the capitalization of it, you can contact
accounts@ppy.sh with the details and they will help you change your username.