Yes it’s IP address will change as you move between geographical locations. Depending on your location your phone will connect to different servers and all those servers will use different IP addresses.
Think of it like this; in a normal LAN, you connect through a router at 192.168.1.1, so your default gateway for computers on your network is 192.168.1.1
The routers default gateway is 184.108.40.206, which is a server owned by your ISP, and your ISP assigns you an external IP address like 220.127.116.11
Your router also assigns internal IP addresses to computers on your network.
All your internal computers connect to the router and the router forwards the traffic out onto the WWW through 18.104.22.168 and the IP address that users on the WWW see for any traffic that comes from any computer on your network will be 22.214.171.124
Now, you could go anywhere in the country and use the same gateway address assigned to you by your ISP and it will work, it might be slower because the gateway will be further away from you, but you will be able to connect to it.
Now with a mobile, you can’t simply use an IP as a gateway, because you might not always be in range of one specific gateway.
So mobile networks use APN (Access Point Names). APN works like DNS and assigns a host name to an IP. So what happens is that all your mobile’s gateways, which all have different IP addresses across the country, use the same APN.
So depending on where you are you could be connecting to any one of many servers and that server could be using any external IP address and could assign your phone any internal IP address.
If you want to keep the same IP address on a phone maybe look at Dynamic DNS which is what people with dynamic external IP addresses use to give themselves a static address. I know DDNS is available on Android phones so I’m sure the iPhone and/or Blackberry can use it as well.