Your ISP controls that. In most cases, it changes on a pretty regular basis on it's own (most ISPs give dynamic IPs for home/personal accounts, static IPs cost extra and usually require a business type account).
If you want a different IP because of Privacy reasons you could always use a Proxy Server to hide your IP Address, although this would mean making your own Proxy Server to how you would like it, I would recommend contacting your ISP.
Look up IP spoofing. There maybe software that will spoof it for you in the way you like, otherwise, if you're a programmer, I use Scapy in python, that allows you to forge packets to every detail including the headers.
If you just want to conceal your IP, Tor is free, but needs to be configured properly, otherwise only your traffic going through your browser is proxified. There are a load of proxies out there for all kind of things, but make sure the proxy you get will anonymize you in the particular network protocol you want.