Actually an ISP is an Internet Service Provider, i.e. the company or business that provides you with internet access you pay for.
You can't change your ISP unless you opt out of the contract you signed on with, or if they don't provide a contract on sign-up, if you cancel and or leave their service.
You cannot change your ISP with an application.
ISPs are businesses that make money serving you the internet.
You're talking about an IP Address, i.e. the series of numbers the ISP provider assigns your PC to access the internet, which is usually temporary.
Wikipedia does a decent explanation of what an IP address is :
en.wikipedia.org/wiki/IP_address
As for AnonymoX, it changes the IP address, or designates you a new one, as is explained on their webpage.
The App does not change your ISP.
That costs money, i.e usually a contract cancellation fee.
~ Pyre