I'm wondering if there is an option somewhere that will allow my IP address to change every time I login to my server.
Anyone know if this is possible?
No. Well, possible. You would have to pay for some more IP addresses, then write a script to bind one to the interface. With IPv6 you could do this, as you are allocated an ipv6/64.
But.... why? And how will you know what IP to connect to, if it's always changing?